Finite Math Examples

$\frac{21820}{x (18) + y (25)} = 940$

Step 1

Factor each term.

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Step 1.1

Move $18$ to the left of $x$ .

$\frac{21820}{18 x + y (25)} = 940$

Step 1.2

Move $25$ to the left of $y$ .

$\frac{21820}{18 x + 25 y} = 940$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$18 x + 25 y, 1$

Step 2.2

Remove parentheses.

$18 x + 25 y, 1$

Step 2.3

The LCM of one and any expression is the expression.

$18 x + 25 y$

Step 3

Multiply each term in $\frac{21820}{18 x + 25 y} = 940$ by $18 x + 25 y$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{21820}{18 x + 25 y} = 940$ by $18 x + 25 y$ .

$\frac{21820}{18 x + 25 y} (18 x + 25 y) = 940 (18 x + 25 y)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $18 x + 25 y$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{21820}{18 x + 25 y} (18 x + 25 y) = 940 (18 x + 25 y)$

Step 3.2.1.2

Rewrite the expression.

$21820 = 940 (18 x + 25 y)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$21820 = 940 (18 x) + 940 (25 y)$

Step 3.3.2

Multiply.

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Step 3.3.2.1

Multiply $18$ by $940$ .

$21820 = 16920 x + 940 (25 y)$

Step 3.3.2.2

Multiply $25$ by $940$ .

$21820 = 16920 x + 23500 y$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $16920 x + 23500 y = 21820$ .

$16920 x + 23500 y = 21820$

Step 4.2

Subtract $23500 y$ from both sides of the equation.

$16920 x = 21820 - 23500 y$

Step 4.3

Divide each term in $16920 x = 21820 - 23500 y$ by $16920$ and simplify.

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Step 4.3.1

Divide each term in $16920 x = 21820 - 23500 y$ by $16920$ .

$\frac{16920 x}{16920} = \frac{21820}{16920} + \frac{- 23500 y}{16920}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $16920$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{16920 x}{16920} = \frac{21820}{16920} + \frac{- 23500 y}{16920}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{21820}{16920} + \frac{- 23500 y}{16920}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Simplify each term.

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Step 4.3.3.1.1

Cancel the common factor of $21820$ and $16920$ .

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Step 4.3.3.1.1.1

Factor $20$ out of $21820$ .

$x = \frac{20 (1091)}{16920} + \frac{- 23500 y}{16920}$

Step 4.3.3.1.1.2

Cancel the common factors.

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Step 4.3.3.1.1.2.1

Factor $20$ out of $16920$ .

$x = \frac{20 \cdot 1091}{20 \cdot 846} + \frac{- 23500 y}{16920}$

Step 4.3.3.1.1.2.2

Cancel the common factor.

$x = \frac{20 \cdot 1091}{20 \cdot 846} + \frac{- 23500 y}{16920}$

Step 4.3.3.1.1.2.3

Rewrite the expression.

$x = \frac{1091}{846} + \frac{- 23500 y}{16920}$

Step 4.3.3.1.2

Cancel the common factor of $- 23500$ and $16920$ .

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Step 4.3.3.1.2.1

Factor $940$ out of $- 23500 y$ .

$x = \frac{1091}{846} + \frac{940 (- 25 y)}{16920}$

Step 4.3.3.1.2.2

Cancel the common factors.

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Step 4.3.3.1.2.2.1

Factor $940$ out of $16920$ .

$x = \frac{1091}{846} + \frac{940 (- 25 y)}{940 (18)}$

Step 4.3.3.1.2.2.2

Cancel the common factor.

$x = \frac{1091}{846} + \frac{940 (- 25 y)}{940 \cdot 18}$

Step 4.3.3.1.2.2.3

Rewrite the expression.

$x = \frac{1091}{846} + \frac{- 25 y}{18}$

Step 4.3.3.1.3

Move the negative in front of the fraction.

$x = \frac{1091}{846} - \frac{25 y}{18}$