Finite Math Examples

$x + 2 y + 2 z = 45000$ , $0.1 x + 0.07 y + 0.075 z = 3660$

Step 1

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

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Step 1.1

Subtract $2 y$ from both sides of the equation.

$x + 2 z = 45000 - 2 y$

$0.1 x + 0.07 y + 0.075 z = 3660$

Step 1.2

Subtract $2 z$ from both sides of the equation.

$x = 45000 - 2 y - 2 z$

$0.1 x + 0.07 y + 0.075 z = 3660$

$x = 45000 - 2 y - 2 z$

$0.1 x + 0.07 y + 0.075 z = 3660$

Step 2

Solve the equation for $z$ .

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Step 2.1

Simplify $0.1 (45000 - 2 y - 2 z) + 0.07 y + 0.075 z$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Apply the distributive property.

$0.1 \cdot 45000 + 0.1 (- 2 y) + 0.1 (- 2 z) + 0.07 y + 0.075 z = 3660$

$x = 45000 - 2 y - 2 z$

Step 2.1.1.2

Simplify.

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Step 2.1.1.2.1

Multiply $0.1$ by $45000$ .

$4500 + 0.1 (- 2 y) + 0.1 (- 2 z) + 0.07 y + 0.075 z = 3660$

$x = 45000 - 2 y - 2 z$

Step 2.1.1.2.2

Multiply $- 2$ by $0.1$ .

$4500 - 0.2 y + 0.1 (- 2 z) + 0.07 y + 0.075 z = 3660$

$x = 45000 - 2 y - 2 z$

Step 2.1.1.2.3

Multiply $- 2$ by $0.1$ .

$4500 - 0.2 y - 0.2 z + 0.07 y + 0.075 z = 3660$

$x = 45000 - 2 y - 2 z$

$4500 - 0.2 y - 0.2 z + 0.07 y + 0.075 z = 3660$

$x = 45000 - 2 y - 2 z$

$4500 - 0.2 y - 0.2 z + 0.07 y + 0.075 z = 3660$

$x = 45000 - 2 y - 2 z$

Step 2.1.2

Simplify by adding terms.

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Step 2.1.2.1

Add $- 0.2 y$ and $0.07 y$ .

$4500 - 0.13 y - 0.2 z + 0.075 z = 3660$

$x = 45000 - 2 y - 2 z$

Step 2.1.2.2

Add $- 0.2 z$ and $0.075 z$ .

$4500 - 0.13 y - 0.125 z = 3660$

$x = 45000 - 2 y - 2 z$

$4500 - 0.13 y - 0.125 z = 3660$

$x = 45000 - 2 y - 2 z$

$4500 - 0.13 y - 0.125 z = 3660$

$x = 45000 - 2 y - 2 z$

Step 2.2

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

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Step 2.2.1

Subtract $4500$ from both sides of the equation.

$- 0.13 y - 0.125 z = 3660 - 4500$

$x = 45000 - 2 y - 2 z$

Step 2.2.2

Add $0.13 y$ to both sides of the equation.

$- 0.125 z = 3660 - 4500 + 0.13 y$

$x = 45000 - 2 y - 2 z$

Step 2.2.3

Subtract $4500$ from $3660$ .

$- 0.125 z = - 840 + 0.13 y$

$x = 45000 - 2 y - 2 z$

$- 0.125 z = - 840 + 0.13 y$

$x = 45000 - 2 y - 2 z$

Step 2.3

Divide each term in $- 0.125 z = - 840 + 0.13 y$ by $- 0.125$ and simplify.

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Step 2.3.1

Divide each term in $- 0.125 z = - 840 + 0.13 y$ by $- 0.125$ .

$\frac{- 0.125 z}{- 0.125} = \frac{- 840}{- 0.125} + \frac{0.13 y}{- 0.125}$

$x = 45000 - 2 y - 2 z$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 0.125$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 0.125 z}{- 0.125} = \frac{- 840}{- 0.125} + \frac{0.13 y}{- 0.125}$

$x = 45000 - 2 y - 2 z$

Step 2.3.2.1.2

Divide $z$ by $1$ .

$z = \frac{- 840}{- 0.125} + \frac{0.13 y}{- 0.125}$

$x = 45000 - 2 y - 2 z$

$z = \frac{- 840}{- 0.125} + \frac{0.13 y}{- 0.125}$

$x = 45000 - 2 y - 2 z$

$z = \frac{- 840}{- 0.125} + \frac{0.13 y}{- 0.125}$

$x = 45000 - 2 y - 2 z$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Simplify each term.

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Step 2.3.3.1.1

Divide $- 840$ by $- 0.125$ .

$z = 6720 + \frac{0.13 y}{- 0.125}$

$x = 45000 - 2 y - 2 z$

Step 2.3.3.1.2

Move the negative in front of the fraction.

$z = 6720 - \frac{0.13 y}{0.125}$

$x = 45000 - 2 y - 2 z$

Step 2.3.3.1.3

Factor $0.13$ out of $0.13 y$ .

$z = 6720 - \frac{0.13 (y)}{0.125}$

$x = 45000 - 2 y - 2 z$

Step 2.3.3.1.4

Factor $0.125$ out of $0.125$ .

$z = 6720 - \frac{0.13 (y)}{0.125 (1)}$

$x = 45000 - 2 y - 2 z$

Step 2.3.3.1.5

Separate fractions.

$z = 6720 - (\frac{0.13}{0.125} \cdot \frac{y}{1})$

$x = 45000 - 2 y - 2 z$

Step 2.3.3.1.6

Divide $0.13$ by $0.125$ .

$z = 6720 - (1.04 (\frac{y}{1}))$

$x = 45000 - 2 y - 2 z$

Step 2.3.3.1.7

Divide $y$ by $1$ .

$z = 6720 - (1.04 y)$

$x = 45000 - 2 y - 2 z$

Step 2.3.3.1.8

Multiply $1.04$ by $- 1$ .

$z = 6720 - 1.04 y$

$x = 45000 - 2 y - 2 z$

$z = 6720 - 1.04 y$

$x = 45000 - 2 y - 2 z$

$z = 6720 - 1.04 y$

$x = 45000 - 2 y - 2 z$

$z = 6720 - 1.04 y$

$x = 45000 - 2 y - 2 z$

$z = 6720 - 1.04 y$

$x = 45000 - 2 y - 2 z$

Step 3

Simplify the right side.

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Step 3.1

Simplify $45000 - 2 y - 2 (6720 - 1.04 y)$ .

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Step 3.1.1

Simplify each term.

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Step 3.1.1.1

Apply the distributive property.

$x = 45000 - 2 y - 2 \cdot 6720 - 2 (- 1.04 y)$

$z = 6720 - 1.04 y$

Step 3.1.1.2

Multiply $- 2$ by $6720$ .

$x = 45000 - 2 y - 13440 - 2 (- 1.04 y)$

$z = 6720 - 1.04 y$

Step 3.1.1.3

Multiply $- 1.04$ by $- 2$ .

$x = 45000 - 2 y - 13440 + 2.08 y$

$z = 6720 - 1.04 y$

$x = 45000 - 2 y - 13440 + 2.08 y$

$z = 6720 - 1.04 y$

Step 3.1.2

Simplify by adding terms.

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Step 3.1.2.1

Subtract $13440$ from $45000$ .

$x = - 2 y + 31560 + 2.08 y$

$z = 6720 - 1.04 y$

Step 3.1.2.2

Add $- 2 y$ and $2.08 y$ .

$x = 0.08 y + 31560$

$z = 6720 - 1.04 y$

$x = 0.08 y + 31560$

$z = 6720 - 1.04 y$

$x = 0.08 y + 31560$

$z = 6720 - 1.04 y$

$x = 0.08 y + 31560$

$z = 6720 - 1.04 y$

Step 4

Simplify the right side.

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Step 4.1

Reorder $6720$ and $- 1.04 y$ .

$z = - 1.04 y + 6720$

$x = 0.08 y + 31560$

$z = - 1.04 y + 6720$

$x = 0.08 y + 31560$