Finite Math Examples

$35 x + 70 y + 175 d + 70 w = 2240$ , $40 x + 40 y + 80 d + 70 w = 1120$ , $40 x + 30 y + 70 d + 10 w = 920$ , $w = 1$

Step 1

Replace all occurrences of $w$ with $1$ in each equation.

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Step 1.1

Replace all occurrences of $w$ in $35 x + 70 y + 175 d + 70 w = 2240$ with $1$ .

$35 x + 70 y + 175 d + 70 (1) = 2240$

$w = 1$

$40 x + 40 y + 80 d + 70 w = 1120$

$40 x + 30 y + 70 d + 10 w = 920$

Step 1.2

Simplify the left side.

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Step 1.2.1

Multiply $70$ by $1$ .

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$40 x + 40 y + 80 d + 70 w = 1120$

$40 x + 30 y + 70 d + 10 w = 920$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$40 x + 40 y + 80 d + 70 w = 1120$

$40 x + 30 y + 70 d + 10 w = 920$

Step 1.3

Replace all occurrences of $w$ in $40 x + 40 y + 80 d + 70 w = 1120$ with $1$ .

$40 x + 40 y + 80 d + 70 (1) = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$40 x + 30 y + 70 d + 10 w = 920$

Step 1.4

Simplify the left side.

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Step 1.4.1

Multiply $70$ by $1$ .

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$40 x + 30 y + 70 d + 10 w = 920$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$40 x + 30 y + 70 d + 10 w = 920$

Step 1.5

Replace all occurrences of $w$ in $40 x + 30 y + 70 d + 10 w = 920$ with $1$ .

$40 x + 30 y + 70 d + 10 (1) = 920$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 1.6

Simplify the left side.

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Step 1.6.1

Multiply $10$ by $1$ .

$40 x + 30 y + 70 d + 10 = 920$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$40 x + 30 y + 70 d + 10 = 920$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$40 x + 30 y + 70 d + 10 = 920$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2

Solve for $x$ in $40 x + 30 y + 70 d + 10 = 920$ .

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Step 2.1

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1.1

Subtract $30 y$ from both sides of the equation.

$40 x + 70 d + 10 = 920 - 30 y$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.1.2

Subtract $70 d$ from both sides of the equation.

$40 x + 10 = 920 - 30 y - 70 d$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.1.3

Subtract $10$ from both sides of the equation.

$40 x = 920 - 30 y - 70 d - 10$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.1.4

Subtract $10$ from $920$ .

$40 x = - 30 y - 70 d + 910$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$40 x = - 30 y - 70 d + 910$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.2

Divide each term in $40 x = - 30 y - 70 d + 910$ by $40$ and simplify.

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Step 2.2.1

Divide each term in $40 x = - 30 y - 70 d + 910$ by $40$ .

$\frac{40 x}{40} = \frac{- 30 y}{40} + \frac{- 70 d}{40} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $40$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{40 x}{40} = \frac{- 30 y}{40} + \frac{- 70 d}{40} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 30 y}{40} + \frac{- 70 d}{40} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$x = \frac{- 30 y}{40} + \frac{- 70 d}{40} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$x = \frac{- 30 y}{40} + \frac{- 70 d}{40} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Cancel the common factor of $- 30$ and $40$ .

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Step 2.2.3.1.1.1

Factor $10$ out of $- 30 y$ .

$x = \frac{10 (- 3 y)}{40} + \frac{- 70 d}{40} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.2.3.1.1.2

Cancel the common factors.

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Step 2.2.3.1.1.2.1

Factor $10$ out of $40$ .

$x = \frac{10 (- 3 y)}{10 (4)} + \frac{- 70 d}{40} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.2.3.1.1.2.2

Cancel the common factor.

$x = \frac{10 (- 3 y)}{10 \cdot 4} + \frac{- 70 d}{40} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.2.3.1.1.2.3

Rewrite the expression.

$x = \frac{- 3 y}{4} + \frac{- 70 d}{40} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$x = \frac{- 3 y}{4} + \frac{- 70 d}{40} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$x = \frac{- 3 y}{4} + \frac{- 70 d}{40} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.2.3.1.2

Move the negative in front of the fraction.

$x = - \frac{3 y}{4} + \frac{- 70 d}{40} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.2.3.1.3

Cancel the common factor of $- 70$ and $40$ .

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Step 2.2.3.1.3.1

Factor $10$ out of $- 70 d$ .

$x = - \frac{3 y}{4} + \frac{10 (- 7 d)}{40} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.2.3.1.3.2

Cancel the common factors.

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Step 2.2.3.1.3.2.1

Factor $10$ out of $40$ .

$x = - \frac{3 y}{4} + \frac{10 (- 7 d)}{10 (4)} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.2.3.1.3.2.2

Cancel the common factor.

$x = - \frac{3 y}{4} + \frac{10 (- 7 d)}{10 \cdot 4} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.2.3.1.3.2.3

Rewrite the expression.

$x = - \frac{3 y}{4} + \frac{- 7 d}{4} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$x = - \frac{3 y}{4} + \frac{- 7 d}{4} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$x = - \frac{3 y}{4} + \frac{- 7 d}{4} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.2.3.1.4

Move the negative in front of the fraction.

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{910}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.2.3.1.5

Cancel the common factor of $910$ and $40$ .

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Step 2.2.3.1.5.1

Factor $10$ out of $910$ .

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{10 (91)}{40}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.2.3.1.5.2

Cancel the common factors.

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Step 2.2.3.1.5.2.1

Factor $10$ out of $40$ .

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{10 \cdot 91}{10 \cdot 4}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.2.3.1.5.2.2

Cancel the common factor.

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{10 \cdot 91}{10 \cdot 4}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 2.2.3.1.5.2.3

Rewrite the expression.

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$40 x + 40 y + 80 d + 70 = 1120$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3

Replace all occurrences of $x$ with $- \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$ in each equation.

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Step 3.1

Replace all occurrences of $x$ in $40 x + 40 y + 80 d + 70 = 1120$ with $- \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$ .

$40 (- \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}) + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify $40 (- \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}) + 40 y + 80 d + 70$ .

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Step 3.2.1.1

Simplify each term.

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Step 3.2.1.1.1

Apply the distributive property.

$40 (- \frac{3 y}{4}) + 40 (- \frac{7 d}{4}) + 40 (\frac{91}{4}) + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2.1.1.2

Simplify.

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Step 3.2.1.1.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1.2.1.1

Move the leading negative in $- \frac{3 y}{4}$ into the numerator.

$40 (\frac{- 3 y}{4}) + 40 (- \frac{7 d}{4}) + 40 (\frac{91}{4}) + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2.1.1.2.1.2

Factor $4$ out of $40$ .

$4 (10) (\frac{- 3 y}{4}) + 40 (- \frac{7 d}{4}) + 40 (\frac{91}{4}) + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2.1.1.2.1.3

Cancel the common factor.

$4 \cdot (10 (\frac{- 3 y}{4})) + 40 (- \frac{7 d}{4}) + 40 (\frac{91}{4}) + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2.1.1.2.1.4

Rewrite the expression.

$10 (- 3 y) + 40 (- \frac{7 d}{4}) + 40 (\frac{91}{4}) + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$10 (- 3 y) + 40 (- \frac{7 d}{4}) + 40 (\frac{91}{4}) + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2.1.1.2.2

Multiply $- 3$ by $10$ .

$- 30 y + 40 (- \frac{7 d}{4}) + 40 (\frac{91}{4}) + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2.1.1.2.3

Cancel the common factor of $4$ .

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Step 3.2.1.1.2.3.1

Move the leading negative in $- \frac{7 d}{4}$ into the numerator.

$- 30 y + 40 (\frac{- 7 d}{4}) + 40 (\frac{91}{4}) + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2.1.1.2.3.2

Factor $4$ out of $40$ .

$- 30 y + 4 (10) (\frac{- 7 d}{4}) + 40 (\frac{91}{4}) + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2.1.1.2.3.3

Cancel the common factor.

$- 30 y + 4 \cdot (10 (\frac{- 7 d}{4})) + 40 (\frac{91}{4}) + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2.1.1.2.3.4

Rewrite the expression.

$- 30 y + 10 (- 7 d) + 40 (\frac{91}{4}) + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$- 30 y + 10 (- 7 d) + 40 (\frac{91}{4}) + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2.1.1.2.4

Multiply $- 7$ by $10$ .

$- 30 y - 70 d + 40 (\frac{91}{4}) + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2.1.1.2.5

Cancel the common factor of $4$ .

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Step 3.2.1.1.2.5.1

Factor $4$ out of $40$ .

$- 30 y - 70 d + 4 (10) (\frac{91}{4}) + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2.1.1.2.5.2

Cancel the common factor.

$- 30 y - 70 d + 4 \cdot (10 (\frac{91}{4})) + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2.1.1.2.5.3

Rewrite the expression.

$- 30 y - 70 d + 10 \cdot 91 + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$- 30 y - 70 d + 10 \cdot 91 + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2.1.1.2.6

Multiply $10$ by $91$ .

$- 30 y - 70 d + 910 + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$- 30 y - 70 d + 910 + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$- 30 y - 70 d + 910 + 40 y + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2.1.2

Simplify by adding terms.

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Step 3.2.1.2.1

Add $- 30 y$ and $40 y$ .

$10 y - 70 d + 910 + 80 d + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2.1.2.2

Add $- 70 d$ and $80 d$ .

$10 y + 10 d + 910 + 70 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.2.1.2.3

Add $910$ and $70$ .

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$35 x + 70 y + 175 d + 70 = 2240$

$w = 1$

Step 3.3

Replace all occurrences of $x$ in $35 x + 70 y + 175 d + 70 = 2240$ with $- \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$ .

$35 (- \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}) + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4

Simplify the left side.

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Step 3.4.1

Simplify $35 (- \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}) + 70 y + 175 d + 70$ .

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Step 3.4.1.1

Simplify each term.

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Step 3.4.1.1.1

Apply the distributive property.

$35 (- \frac{3 y}{4}) + 35 (- \frac{7 d}{4}) + 35 (\frac{91}{4}) + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.1.2

Simplify.

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Step 3.4.1.1.2.1

Multiply $35 (- \frac{3 y}{4})$ .

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Step 3.4.1.1.2.1.1

Multiply $- 1$ by $35$ .

$- 35 \frac{3 y}{4} + 35 (- \frac{7 d}{4}) + 35 (\frac{91}{4}) + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.1.2.1.2

Combine $- 35$ and $\frac{3 y}{4}$ .

$\frac{- 35 (3 y)}{4} + 35 (- \frac{7 d}{4}) + 35 (\frac{91}{4}) + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.1.2.1.3

Multiply $3$ by $- 35$ .

$\frac{- 105 y}{4} + 35 (- \frac{7 d}{4}) + 35 (\frac{91}{4}) + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$\frac{- 105 y}{4} + 35 (- \frac{7 d}{4}) + 35 (\frac{91}{4}) + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.1.2.2

Multiply $35 (- \frac{7 d}{4})$ .

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Step 3.4.1.1.2.2.1

Multiply $- 1$ by $35$ .

$\frac{- 105 y}{4} - 35 \frac{7 d}{4} + 35 (\frac{91}{4}) + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.1.2.2.2

Combine $- 35$ and $\frac{7 d}{4}$ .

$\frac{- 105 y}{4} + \frac{- 35 (7 d)}{4} + 35 (\frac{91}{4}) + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.1.2.2.3

Multiply $7$ by $- 35$ .

$\frac{- 105 y}{4} + \frac{- 245 d}{4} + 35 (\frac{91}{4}) + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$\frac{- 105 y}{4} + \frac{- 245 d}{4} + 35 (\frac{91}{4}) + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.1.2.3

Multiply $35 (\frac{91}{4})$ .

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Step 3.4.1.1.2.3.1

Combine $35$ and $\frac{91}{4}$ .

$\frac{- 105 y}{4} + \frac{- 245 d}{4} + \frac{35 \cdot 91}{4} + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.1.2.3.2

Multiply $35$ by $91$ .

$\frac{- 105 y}{4} + \frac{- 245 d}{4} + \frac{3185}{4} + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$\frac{- 105 y}{4} + \frac{- 245 d}{4} + \frac{3185}{4} + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$\frac{- 105 y}{4} + \frac{- 245 d}{4} + \frac{3185}{4} + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.1.3

Simplify each term.

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Step 3.4.1.1.3.1

Move the negative in front of the fraction.

$- \frac{105 y}{4} + \frac{- 245 d}{4} + \frac{3185}{4} + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.1.3.2

Move the negative in front of the fraction.

$- \frac{105 y}{4} - \frac{245 d}{4} + \frac{3185}{4} + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$- \frac{105 y}{4} - \frac{245 d}{4} + \frac{3185}{4} + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$- \frac{105 y}{4} - \frac{245 d}{4} + \frac{3185}{4} + 70 y + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.2

To write $70 y$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{245 d}{4} + \frac{3185}{4} - \frac{105 y}{4} + 70 y \cdot \frac{4}{4} + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.3

Combine $70 y$ and $\frac{4}{4}$ .

$- \frac{245 d}{4} + \frac{3185}{4} - \frac{105 y}{4} + \frac{70 y \cdot 4}{4} + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.4

Combine the numerators over the common denominator.

$- \frac{245 d}{4} + \frac{3185}{4} + \frac{- 105 y + 70 y \cdot 4}{4} + 175 d + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.5

Combine the numerators over the common denominator.

$175 d + 70 + \frac{- 245 d + 3185 - 105 y + 70 y \cdot 4}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.6

Multiply $4$ by $70$ .

$175 d + 70 + \frac{- 245 d + 3185 - 105 y + 280 y}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.7

Add $- 105 y$ and $280 y$ .

$175 d + 70 + \frac{- 245 d + 3185 + 175 y}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.8

Factor $35$ out of $- 245 d + 3185 + 175 y$ .

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Step 3.4.1.8.1

Factor $35$ out of $- 245 d$ .

$175 d + 70 + \frac{35 (- 7 d) + 3185 + 175 y}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.8.2

Factor $35$ out of $3185$ .

$175 d + 70 + \frac{35 (- 7 d) + 35 (91) + 175 y}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.8.3

Factor $35$ out of $175 y$ .

$175 d + 70 + \frac{35 (- 7 d) + 35 (91) + 35 (5 y)}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.8.4

Factor $35$ out of $35 (- 7 d) + 35 (91)$ .

$175 d + 70 + \frac{35 (- 7 d + 91) + 35 (5 y)}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.8.5

Factor $35$ out of $35 (- 7 d + 91) + 35 (5 y)$ .

$175 d + 70 + \frac{35 (- 7 d + 91 + 5 y)}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$175 d + 70 + \frac{35 (- 7 d + 91 + 5 y)}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.9

To write $175 d$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$175 d \cdot \frac{4}{4} + \frac{35 (- 7 d + 91 + 5 y)}{4} + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.10

Simplify terms.

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Step 3.4.1.10.1

Combine $175 d$ and $\frac{4}{4}$ .

$\frac{175 d \cdot 4}{4} + \frac{35 (- 7 d + 91 + 5 y)}{4} + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.10.2

Combine the numerators over the common denominator.

$\frac{175 d \cdot 4 + 35 (- 7 d + 91 + 5 y)}{4} + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$\frac{175 d \cdot 4 + 35 (- 7 d + 91 + 5 y)}{4} + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.11

Simplify the numerator.

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Step 3.4.1.11.1

Factor $35$ out of $175 d \cdot 4 + 35 (- 7 d + 91 + 5 y)$ .

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Step 3.4.1.11.1.1

Factor $35$ out of $175 d \cdot 4$ .

$\frac{35 (5 d \cdot 4) + 35 (- 7 d + 91 + 5 y)}{4} + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.11.1.2

Factor $35$ out of $35 (5 d \cdot 4) + 35 (- 7 d + 91 + 5 y)$ .

$\frac{35 (5 d \cdot 4 - 7 d + 91 + 5 y)}{4} + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$\frac{35 (5 d \cdot 4 - 7 d + 91 + 5 y)}{4} + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.11.2

Multiply $4$ by $5$ .

$\frac{35 (20 d - 7 d + 91 + 5 y)}{4} + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.11.3

Subtract $7 d$ from $20 d$ .

$\frac{35 (13 d + 91 + 5 y)}{4} + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$\frac{35 (13 d + 91 + 5 y)}{4} + 70 = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.12

To write $70$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{35 (13 d + 91 + 5 y)}{4} + 70 \cdot \frac{4}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.13

Simplify terms.

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Step 3.4.1.13.1

Combine $70$ and $\frac{4}{4}$ .

$\frac{35 (13 d + 91 + 5 y)}{4} + \frac{70 \cdot 4}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.13.2

Combine the numerators over the common denominator.

$\frac{35 (13 d + 91 + 5 y) + 70 \cdot 4}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$\frac{35 (13 d + 91 + 5 y) + 70 \cdot 4}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.14

Simplify the numerator.

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Step 3.4.1.14.1

Factor $35$ out of $35 (13 d + 91 + 5 y) + 70 \cdot 4$ .

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Step 3.4.1.14.1.1

Factor $35$ out of $70 \cdot 4$ .

$\frac{35 (13 d + 91 + 5 y) + 35 (2 \cdot 4)}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.14.1.2

Factor $35$ out of $35 (13 d + 91 + 5 y) + 35 (2 \cdot 4)$ .

$\frac{35 (13 d + 91 + 5 y + 2 \cdot 4)}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$\frac{35 (13 d + 91 + 5 y + 2 \cdot 4)}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.14.2

Multiply $2$ by $4$ .

$\frac{35 (13 d + 91 + 5 y + 8)}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 3.4.1.14.3

Add $91$ and $8$ .

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$10 y + 10 d + 980 = 1120$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 4

Solve for $y$ in $10 y + 10 d + 980 = 1120$ .

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Step 4.1

Move all terms not containing $y$ to the right side of the equation.

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Step 4.1.1

Subtract $10 d$ from both sides of the equation.

$10 y + 980 = 1120 - 10 d$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 4.1.2

Subtract $980$ from both sides of the equation.

$10 y = 1120 - 10 d - 980$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 4.1.3

Subtract $980$ from $1120$ .

$10 y = - 10 d + 140$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$10 y = - 10 d + 140$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 4.2

Divide each term in $10 y = - 10 d + 140$ by $10$ and simplify.

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Step 4.2.1

Divide each term in $10 y = - 10 d + 140$ by $10$ .

$\frac{10 y}{10} = \frac{- 10 d}{10} + \frac{140}{10}$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $10$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{10 y}{10} = \frac{- 10 d}{10} + \frac{140}{10}$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 10 d}{10} + \frac{140}{10}$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$y = \frac{- 10 d}{10} + \frac{140}{10}$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$y = \frac{- 10 d}{10} + \frac{140}{10}$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Simplify each term.

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Step 4.2.3.1.1

Cancel the common factor of $- 10$ and $10$ .

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Step 4.2.3.1.1.1

Factor $10$ out of $- 10 d$ .

$y = \frac{10 (- d)}{10} + \frac{140}{10}$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 4.2.3.1.1.2

Cancel the common factors.

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Step 4.2.3.1.1.2.1

Factor $10$ out of $10$ .

$y = \frac{10 (- d)}{10 (1)} + \frac{140}{10}$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 4.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{10 (- d)}{10 \cdot 1} + \frac{140}{10}$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 4.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{- d}{1} + \frac{140}{10}$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 4.2.3.1.1.2.4

Divide $- d$ by $1$ .

$y = - d + \frac{140}{10}$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$y = - d + \frac{140}{10}$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$y = - d + \frac{140}{10}$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 4.2.3.1.2

Divide $140$ by $10$ .

$y = - d + 14$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$y = - d + 14$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$y = - d + 14$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$y = - d + 14$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$y = - d + 14$

$\frac{35 (13 d + 5 y + 99)}{4} = 2240$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 5

Replace all occurrences of $y$ with $- d + 14$ in each equation.

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Step 5.1

Replace all occurrences of $y$ in $\frac{35 (13 d + 5 y + 99)}{4} = 2240$ with $- d + 14$ .

$\frac{35 (13 d + 5 (- d + 14) + 99)}{4} = 2240$

$y = - d + 14$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 5.2

Simplify the left side.

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Step 5.2.1

Simplify the numerator.

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Step 5.2.1.1

Apply the distributive property.

$\frac{35 (13 d + 5 (- d) + 5 \cdot 14 + 99)}{4} = 2240$

$y = - d + 14$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 5.2.1.2

Multiply $- 1$ by $5$ .

$\frac{35 (13 d - 5 d + 5 \cdot 14 + 99)}{4} = 2240$

$y = - d + 14$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 5.2.1.3

Multiply $5$ by $14$ .

$\frac{35 (13 d - 5 d + 70 + 99)}{4} = 2240$

$y = - d + 14$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 5.2.1.4

Subtract $5 d$ from $13 d$ .

$\frac{35 (8 d + 70 + 99)}{4} = 2240$

$y = - d + 14$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 5.2.1.5

Add $70$ and $99$ .

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$

$w = 1$

Step 5.3

Replace all occurrences of $y$ in $x = - \frac{3 y}{4} - \frac{7 d}{4} + \frac{91}{4}$ with $- d + 14$ .

$x = - \frac{3 (- d + 14)}{4} - \frac{7 d}{4} + \frac{91}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

Step 5.4

Simplify the right side.

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Step 5.4.1

Simplify $- \frac{3 (- d + 14)}{4} - \frac{7 d}{4} + \frac{91}{4}$ .

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Step 5.4.1.1

Combine the numerators over the common denominator.

$x = \frac{- 3 (- d + 14) - 7 d + 91}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

Step 5.4.1.2

Simplify each term.

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Step 5.4.1.2.1

Apply the distributive property.

$x = \frac{- 3 (- d) - 3 \cdot 14 - 7 d + 91}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

Step 5.4.1.2.2

Multiply $- 1$ by $- 3$ .

$x = \frac{3 d - 3 \cdot 14 - 7 d + 91}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

Step 5.4.1.2.3

Multiply $- 3$ by $14$ .

$x = \frac{3 d - 42 - 7 d + 91}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

$x = \frac{3 d - 42 - 7 d + 91}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

Step 5.4.1.3

Simplify terms.

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Step 5.4.1.3.1

Subtract $7 d$ from $3 d$ .

$x = \frac{- 4 d - 42 + 91}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

Step 5.4.1.3.2

Add $- 42$ and $91$ .

$x = \frac{- 4 d + 49}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

Step 5.4.1.3.3

Factor $- 1$ out of $- 4 d$ .

$x = \frac{- (4 d) + 49}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

Step 5.4.1.3.4

Rewrite $49$ as $- 1 (- 49)$ .

$x = \frac{- (4 d) - 1 \cdot - 49}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

Step 5.4.1.3.5

Factor $- 1$ out of $- (4 d) - 1 (- 49)$ .

$x = \frac{- (4 d - 49)}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

Step 5.4.1.3.6

Simplify the expression.

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Step 5.4.1.3.6.1

Rewrite $- (4 d - 49)$ as $- 1 (4 d - 49)$ .

$x = \frac{- 1 (4 d - 49)}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

Step 5.4.1.3.6.2

Move the negative in front of the fraction.

$x = - \frac{4 d - 49}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

$x = - \frac{4 d - 49}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

$x = - \frac{4 d - 49}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

$x = - \frac{4 d - 49}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

$x = - \frac{4 d - 49}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

$x = - \frac{4 d - 49}{4}$

$\frac{35 (8 d + 169)}{4} = 2240$

$y = - d + 14$

$w = 1$

Step 6

Solve for $d$ in $\frac{35 (8 d + 169)}{4} = 2240$ .

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Step 6.1

Multiply both sides by $4$ .

$\frac{35 (8 d + 169)}{4} \cdot 4 = 2240 \cdot 4$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

Step 6.2

Simplify.

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Step 6.2.1

Simplify the left side.

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Step 6.2.1.1

Simplify $\frac{35 (8 d + 169)}{4} \cdot 4$ .

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Step 6.2.1.1.1

Cancel the common factor of $4$ .

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Step 6.2.1.1.1.1

Cancel the common factor.

$\frac{35 (8 d + 169)}{4} \cdot 4 = 2240 \cdot 4$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

Step 6.2.1.1.1.2

Rewrite the expression.

$35 (8 d + 169) = 2240 \cdot 4$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

$35 (8 d + 169) = 2240 \cdot 4$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

Step 6.2.1.1.2

Apply the distributive property.

$35 (8 d) + 35 \cdot 169 = 2240 \cdot 4$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

Step 6.2.1.1.3

Multiply.

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Step 6.2.1.1.3.1

Multiply $8$ by $35$ .

$280 d + 35 \cdot 169 = 2240 \cdot 4$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

Step 6.2.1.1.3.2

Multiply $35$ by $169$ .

$280 d + 5915 = 2240 \cdot 4$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

$280 d + 5915 = 2240 \cdot 4$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

$280 d + 5915 = 2240 \cdot 4$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

$280 d + 5915 = 2240 \cdot 4$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

Step 6.2.2

Simplify the right side.

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Step 6.2.2.1

Multiply $2240$ by $4$ .

$280 d + 5915 = 8960$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

$280 d + 5915 = 8960$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

$280 d + 5915 = 8960$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

Step 6.3

Solve for $d$ .

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Step 6.3.1

Move all terms not containing $d$ to the right side of the equation.

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Step 6.3.1.1

Subtract $5915$ from both sides of the equation.

$280 d = 8960 - 5915$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

Step 6.3.1.2

Subtract $5915$ from $8960$ .

$280 d = 3045$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

$280 d = 3045$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

Step 6.3.2

Divide each term in $280 d = 3045$ by $280$ and simplify.

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Step 6.3.2.1

Divide each term in $280 d = 3045$ by $280$ .

$\frac{280 d}{280} = \frac{3045}{280}$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

Step 6.3.2.2

Simplify the left side.

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Step 6.3.2.2.1

Cancel the common factor of $280$ .

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Step 6.3.2.2.1.1

Cancel the common factor.

$\frac{280 d}{280} = \frac{3045}{280}$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

Step 6.3.2.2.1.2

Divide $d$ by $1$ .

$d = \frac{3045}{280}$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

$d = \frac{3045}{280}$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

$d = \frac{3045}{280}$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

Step 6.3.2.3

Simplify the right side.

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Step 6.3.2.3.1

Cancel the common factor of $3045$ and $280$ .

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Step 6.3.2.3.1.1

Factor $35$ out of $3045$ .

$d = \frac{35 (87)}{280}$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

Step 6.3.2.3.1.2

Cancel the common factors.

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Step 6.3.2.3.1.2.1

Factor $35$ out of $280$ .

$d = \frac{35 \cdot 87}{35 \cdot 8}$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

Step 6.3.2.3.1.2.2

Cancel the common factor.

$d = \frac{35 \cdot 87}{35 \cdot 8}$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

Step 6.3.2.3.1.2.3

Rewrite the expression.

$d = \frac{87}{8}$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

$d = \frac{87}{8}$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

$d = \frac{87}{8}$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

$d = \frac{87}{8}$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

$d = \frac{87}{8}$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

$d = \frac{87}{8}$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

$d = \frac{87}{8}$

$x = - \frac{4 d - 49}{4}$

$y = - d + 14$

$w = 1$

Step 7

Replace all occurrences of $d$ with $\frac{87}{8}$ in each equation.

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Step 7.1

Replace all occurrences of $d$ in $x = - \frac{4 d - 49}{4}$ with $\frac{87}{8}$ .

$x = - \frac{4 (\frac{87}{8}) - 49}{4}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

Step 7.2

Simplify the right side.

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Step 7.2.1

Simplify $- \frac{4 (\frac{87}{8}) - 49}{4}$ .

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Step 7.2.1.1

Simplify the numerator.

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Step 7.2.1.1.1

Cancel the common factor of $4$ .

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Step 7.2.1.1.1.1

Factor $4$ out of $8$ .

$x = - \frac{4 (\frac{87}{4 (2)}) - 49}{4}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

Step 7.2.1.1.1.2

Cancel the common factor.

$x = - \frac{4 (\frac{87}{4 \cdot 2}) - 49}{4}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

Step 7.2.1.1.1.3

Rewrite the expression.

$x = - \frac{\frac{87}{2} - 49}{4}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

$x = - \frac{\frac{87}{2} - 49}{4}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

Step 7.2.1.1.2

To write $- 49$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = - \frac{\frac{87}{2} - 49 \cdot \frac{2}{2}}{4}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

Step 7.2.1.1.3

Combine $- 49$ and $\frac{2}{2}$ .

$x = - \frac{\frac{87}{2} + \frac{- 49 \cdot 2}{2}}{4}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

Step 7.2.1.1.4

Combine the numerators over the common denominator.

$x = - \frac{\frac{87 - 49 \cdot 2}{2}}{4}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

Step 7.2.1.1.5

Simplify the numerator.

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Step 7.2.1.1.5.1

Multiply $- 49$ by $2$ .

$x = - \frac{\frac{87 - 98}{2}}{4}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

Step 7.2.1.1.5.2

Subtract $98$ from $87$ .

$x = - \frac{\frac{- 11}{2}}{4}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

$x = - \frac{\frac{- 11}{2}}{4}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

Step 7.2.1.1.6

Move the negative in front of the fraction.

$x = - \frac{- \frac{11}{2}}{4}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

$x = - \frac{- \frac{11}{2}}{4}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

Step 7.2.1.2

Multiply the numerator by the reciprocal of the denominator.

$x = - (- \frac{11}{2} \cdot \frac{1}{4})$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

Step 7.2.1.3

Multiply $- \frac{11}{2} \cdot \frac{1}{4}$ .

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Step 7.2.1.3.1

Multiply $\frac{1}{4}$ by $\frac{11}{2}$ .

$x = \frac{11}{4 \cdot 2}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

Step 7.2.1.3.2

Multiply $4$ by $2$ .

$x = \frac{11}{8}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

$x = \frac{11}{8}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

Step 7.2.1.4

Multiply $- - \frac{11}{8}$ .

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Step 7.2.1.4.1

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{11}{8})$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

Step 7.2.1.4.2

Multiply $\frac{11}{8}$ by $1$ .

$x = \frac{11}{8}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

$x = \frac{11}{8}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

$x = \frac{11}{8}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

$x = \frac{11}{8}$

$d = \frac{87}{8}$

$y = - d + 14$

$w = 1$

Step 7.3

Replace all occurrences of $d$ in $y = - d + 14$ with $\frac{87}{8}$ .

$y = - (\frac{87}{8}) + 14$

$x = \frac{11}{8}$

$d = \frac{87}{8}$

$w = 1$

Step 7.4

Simplify the right side.

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Step 7.4.1

Simplify $- (\frac{87}{8}) + 14$ .

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Step 7.4.1.1

To write $14$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$y = - \frac{87}{8} + 14 \cdot \frac{8}{8}$

$x = \frac{11}{8}$

$d = \frac{87}{8}$

$w = 1$

Step 7.4.1.2

Combine $14$ and $\frac{8}{8}$ .

$y = - \frac{87}{8} + \frac{14 \cdot 8}{8}$

$x = \frac{11}{8}$

$d = \frac{87}{8}$

$w = 1$

Step 7.4.1.3

Combine the numerators over the common denominator.

$y = \frac{- 87 + 14 \cdot 8}{8}$

$x = \frac{11}{8}$

$d = \frac{87}{8}$

$w = 1$

Step 7.4.1.4

Simplify the numerator.

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Step 7.4.1.4.1

Multiply $14$ by $8$ .

$y = \frac{- 87 + 112}{8}$

$x = \frac{11}{8}$

$d = \frac{87}{8}$

$w = 1$

Step 7.4.1.4.2

Add $- 87$ and $112$ .

$y = \frac{25}{8}$

$x = \frac{11}{8}$

$d = \frac{87}{8}$

$w = 1$

$y = \frac{25}{8}$

$x = \frac{11}{8}$

$d = \frac{87}{8}$

$w = 1$

$y = \frac{25}{8}$

$x = \frac{11}{8}$

$d = \frac{87}{8}$

$w = 1$

$y = \frac{25}{8}$

$x = \frac{11}{8}$

$d = \frac{87}{8}$

$w = 1$

$y = \frac{25}{8}$

$x = \frac{11}{8}$

$d = \frac{87}{8}$

$w = 1$

Step 8

List all of the solutions.

$y = \frac{25}{8}, x = \frac{11}{8}, d = \frac{87}{8}, w = 1$