Finite Math Examples

$p = 300 - \frac{3}{5} q$ , $p = \frac{2}{5} q$

Step 1

Eliminate the equal sides of each equation and combine.

$300 - \frac{3}{5} q = \frac{2}{5} q$

Step 2

Solve $300 - \frac{3}{5} q = \frac{2}{5} q$ for $q$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine $q$ and $\frac{3}{5}$ .

$300 - \frac{q \cdot 3}{5} = \frac{2}{5} q$

Step 2.1.2

Move $3$ to the left of $q$ .

$300 - \frac{3 q}{5} = \frac{2}{5} q$

Step 2.2

Combine $\frac{2}{5}$ and $q$ .

$300 - \frac{3 q}{5} = \frac{2 q}{5}$

Step 2.3

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

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Step 2.3.1

Subtract $\frac{2 q}{5}$ from both sides of the equation.

$300 - \frac{3 q}{5} - \frac{2 q}{5} = 0$

Step 2.3.2

Combine the numerators over the common denominator.

$300 + \frac{- 3 q - 2 q}{5} = 0$

Step 2.3.3

Subtract $2 q$ from $- 3 q$ .

$300 + \frac{- 5 q}{5} = 0$

Step 2.3.4

Cancel the common factor of $- 5$ and $5$ .

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Step 2.3.4.1

Factor $5$ out of $- 5 q$ .

$300 + \frac{5 (- q)}{5} = 0$

Step 2.3.4.2

Cancel the common factors.

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Step 2.3.4.2.1

Factor $5$ out of $5$ .

$300 + \frac{5 (- q)}{5 (1)} = 0$

Step 2.3.4.2.2

Cancel the common factor.

$300 + \frac{5 (- q)}{5 \cdot 1} = 0$

Step 2.3.4.2.3

Rewrite the expression.

$300 + \frac{- q}{1} = 0$

Step 2.3.4.2.4

Divide $- q$ by $1$ .

$300 - q = 0$

Step 2.4

Subtract $300$ from both sides of the equation.

$- q = - 300$

Step 2.5

Divide each term in $- q = - 300$ by $- 1$ and simplify.

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Step 2.5.1

Divide each term in $- q = - 300$ by $- 1$ .

$\frac{- q}{- 1} = \frac{- 300}{- 1}$

Step 2.5.2

Simplify the left side.

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Step 2.5.2.1

Dividing two negative values results in a positive value.

$\frac{q}{1} = \frac{- 300}{- 1}$

Step 2.5.2.2

Divide $q$ by $1$ .

$q = \frac{- 300}{- 1}$

Step 2.5.3

Simplify the right side.

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Step 2.5.3.1

Divide $- 300$ by $- 1$ .

$q = 300$

Step 3

Evaluate $p$ when $q = 300$ .

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Step 3.1

Substitute $300$ for $q$ .

$p = \frac{2}{5} \cdot (300)$

Step 3.2

Substitute $300$ for $q$ in $p = \frac{2}{5} \cdot (300)$ and solve for $p$ .

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Step 3.2.1

Multiply $\frac{2}{5}$ by $300$ .

$p = \frac{2}{5} \cdot 300$

Step 3.2.2

Simplify $\frac{2}{5} \cdot 300$ .

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Step 3.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1

Factor $5$ out of $300$ .

$p = \frac{2}{5} \cdot (5 (60))$

Step 3.2.2.1.2

Cancel the common factor.

$p = \frac{2}{5} \cdot (5 \cdot 60)$

Step 3.2.2.1.3

Rewrite the expression.

$p = 2 \cdot 60$

Step 3.2.2.2

Multiply $2$ by $60$ .

$p = 120$

Step 4

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

$p = 120, q = 300$