Finite Math Examples

$q = - 11000 p + 3600$ , $q = 4000 p + 600$

Step 1

Eliminate the equal sides of each equation and combine.

$- 11000 p + 3600 = 4000 p + 600$

Step 2

Solve $- 11000 p + 3600 = 4000 p + 600$ for $p$ .

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Step 2.1

Move all terms containing $p$ to the left side of the equation.

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Step 2.1.1

Subtract $4000 p$ from both sides of the equation.

$- 11000 p + 3600 - 4000 p = 600$

Step 2.1.2

Subtract $4000 p$ from $- 11000 p$ .

$- 15000 p + 3600 = 600$

Step 2.2

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

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Step 2.2.1

Subtract $3600$ from both sides of the equation.

$- 15000 p = 600 - 3600$

Step 2.2.2

Subtract $3600$ from $600$ .

$- 15000 p = - 3000$

Step 2.3

Divide each term in $- 15000 p = - 3000$ by $- 15000$ and simplify.

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Step 2.3.1

Divide each term in $- 15000 p = - 3000$ by $- 15000$ .

$\frac{- 15000 p}{- 15000} = \frac{- 3000}{- 15000}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 15000$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 15000 p}{- 15000} = \frac{- 3000}{- 15000}$

Step 2.3.2.1.2

Divide $p$ by $1$ .

$p = \frac{- 3000}{- 15000}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Cancel the common factor of $- 3000$ and $- 15000$ .

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Step 2.3.3.1.1

Factor $- 3000$ out of $- 3000$ .

$p = \frac{- 3000 (1)}{- 15000}$

Step 2.3.3.1.2

Cancel the common factors.

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Step 2.3.3.1.2.1

Factor $- 3000$ out of $- 15000$ .

$p = \frac{- 3000 \cdot 1}{- 3000 \cdot 5}$

Step 2.3.3.1.2.2

Cancel the common factor.

$p = \frac{- 3000 \cdot 1}{- 3000 \cdot 5}$

Step 2.3.3.1.2.3

Rewrite the expression.

$p = \frac{1}{5}$

Step 3

Evaluate $q$ when $p = \frac{1}{5}$ .

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Step 3.1

Substitute $\frac{1}{5}$ for $p$ .

$q = 4000 (\frac{1}{5}) + 600$

Step 3.2

Simplify $4000 (\frac{1}{5}) + 600$ .

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Step 3.2.1

Cancel the common factor of $5$ .

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Step 3.2.1.1

Factor $5$ out of $4000$ .

$q = 5 (800) \frac{1}{5} + 600$

Step 3.2.1.2

Cancel the common factor.

$q = 5 \cdot 800 \frac{1}{5} + 600$

Step 3.2.1.3

Rewrite the expression.

$q = 800 + 600$

Step 3.2.2

Add $800$ and $600$ .

$q = 1400$

Step 4

The solution of the system of equations is all the values that make the system true.

$q = 1400, p = \frac{1}{5}$