Finite Math Examples

$b = m - 14$ , $600 b + 1500 m = 81200$

Step 1

Replace all occurrences of $b$ with $m - 14$ in each equation.

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Step 1.1

Replace all occurrences of $b$ in $600 b + 1500 m = 81200$ with $m - 14$ .

$600 (m - 14) + 1500 m = 81200$

$b = m - 14$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $600 (m - 14) + 1500 m$ .

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Apply the distributive property.

$600 m + 600 \cdot - 14 + 1500 m = 81200$

$b = m - 14$

Step 1.2.1.1.2

Multiply $600$ by $- 14$ .

$600 m - 8400 + 1500 m = 81200$

$b = m - 14$

$600 m - 8400 + 1500 m = 81200$

$b = m - 14$

Step 1.2.1.2

Add $600 m$ and $1500 m$ .

$2100 m - 8400 = 81200$

$b = m - 14$

$2100 m - 8400 = 81200$

$b = m - 14$

$2100 m - 8400 = 81200$

$b = m - 14$

$2100 m - 8400 = 81200$

$b = m - 14$

Step 2

Solve for $m$ in $2100 m - 8400 = 81200$ .

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Step 2.1

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

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Step 2.1.1

Add $8400$ to both sides of the equation.

$2100 m = 81200 + 8400$

$b = m - 14$

Step 2.1.2

Add $81200$ and $8400$ .

$2100 m = 89600$

$b = m - 14$

$2100 m = 89600$

$b = m - 14$

Step 2.2

Divide each term in $2100 m = 89600$ by $2100$ and simplify.

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Step 2.2.1

Divide each term in $2100 m = 89600$ by $2100$ .

$\frac{2100 m}{2100} = \frac{89600}{2100}$

$b = m - 14$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $2100$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{2100 m}{2100} = \frac{89600}{2100}$

$b = m - 14$

Step 2.2.2.1.2

Divide $m$ by $1$ .

$m = \frac{89600}{2100}$

$b = m - 14$

$m = \frac{89600}{2100}$

$b = m - 14$

$m = \frac{89600}{2100}$

$b = m - 14$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Cancel the common factor of $89600$ and $2100$ .

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Step 2.2.3.1.1

Factor $700$ out of $89600$ .

$m = \frac{700 (128)}{2100}$

$b = m - 14$

Step 2.2.3.1.2

Cancel the common factors.

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Step 2.2.3.1.2.1

Factor $700$ out of $2100$ .

$m = \frac{700 \cdot 128}{700 \cdot 3}$

$b = m - 14$

Step 2.2.3.1.2.2

Cancel the common factor.

$m = \frac{700 \cdot 128}{700 \cdot 3}$

$b = m - 14$

Step 2.2.3.1.2.3

Rewrite the expression.

$m = \frac{128}{3}$

$b = m - 14$

$m = \frac{128}{3}$

$b = m - 14$

$m = \frac{128}{3}$

$b = m - 14$

$m = \frac{128}{3}$

$b = m - 14$

$m = \frac{128}{3}$

$b = m - 14$

$m = \frac{128}{3}$

$b = m - 14$

Step 3

Replace all occurrences of $m$ with $\frac{128}{3}$ in each equation.

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Step 3.1

Replace all occurrences of $m$ in $b = m - 14$ with $\frac{128}{3}$ .

$b = (\frac{128}{3}) - 14$

$m = \frac{128}{3}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $(\frac{128}{3}) - 14$ .

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Step 3.2.1.1

To write $- 14$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b = \frac{128}{3} - 14 \cdot \frac{3}{3}$

$m = \frac{128}{3}$

Step 3.2.1.2

Combine $- 14$ and $\frac{3}{3}$ .

$b = \frac{128}{3} + \frac{- 14 \cdot 3}{3}$

$m = \frac{128}{3}$

Step 3.2.1.3

Combine the numerators over the common denominator.

$b = \frac{128 - 14 \cdot 3}{3}$

$m = \frac{128}{3}$

Step 3.2.1.4

Simplify the numerator.

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Step 3.2.1.4.1

Multiply $- 14$ by $3$ .

$b = \frac{128 - 42}{3}$

$m = \frac{128}{3}$

Step 3.2.1.4.2

Subtract $42$ from $128$ .

$b = \frac{86}{3}$

$m = \frac{128}{3}$

$b = \frac{86}{3}$

$m = \frac{128}{3}$

$b = \frac{86}{3}$

$m = \frac{128}{3}$

$b = \frac{86}{3}$

$m = \frac{128}{3}$

$b = \frac{86}{3}$

$m = \frac{128}{3}$

Step 4

List all of the solutions.

$b = \frac{86}{3}, m = \frac{128}{3}$