Finite Math Examples

$30 r + 20 p = 17.4$ , $20 r + 12 p = 11.04$ , $10 r + 50 p = x$

Step 1

Rewrite the equation as $x = 10 r + 50 p$ .

$x = 10 r + 50 p$

$30 r + 20 p = 17.4$

$20 r + 12 p = 11.04$

Step 2

Solve for $r$ in $30 r + 20 p = 17.4$ .

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Step 2.1

Subtract $20 p$ from both sides of the equation.

$30 r = 17.4 - 20 p$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

Step 2.2

Divide each term in $30 r = 17.4 - 20 p$ by $30$ and simplify.

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Step 2.2.1

Divide each term in $30 r = 17.4 - 20 p$ by $30$ .

$\frac{30 r}{30} = \frac{17.4}{30} + \frac{- 20 p}{30}$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $30$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{30 r}{30} = \frac{17.4}{30} + \frac{- 20 p}{30}$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

Step 2.2.2.1.2

Divide $r$ by $1$ .

$r = \frac{17.4}{30} + \frac{- 20 p}{30}$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

$r = \frac{17.4}{30} + \frac{- 20 p}{30}$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

$r = \frac{17.4}{30} + \frac{- 20 p}{30}$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Divide $17.4$ by $30$ .

$r = 0.58 + \frac{- 20 p}{30}$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

Step 2.2.3.1.2

Cancel the common factor of $- 20$ and $30$ .

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Step 2.2.3.1.2.1

Factor $10$ out of $- 20 p$ .

$r = 0.58 + \frac{10 (- 2 p)}{30}$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

Step 2.2.3.1.2.2

Cancel the common factors.

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Step 2.2.3.1.2.2.1

Factor $10$ out of $30$ .

$r = 0.58 + \frac{10 (- 2 p)}{10 (3)}$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

Step 2.2.3.1.2.2.2

Cancel the common factor.

$r = 0.58 + \frac{10 (- 2 p)}{10 \cdot 3}$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

Step 2.2.3.1.2.2.3

Rewrite the expression.

$r = 0.58 + \frac{- 2 p}{3}$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

$r = 0.58 + \frac{- 2 p}{3}$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

$r = 0.58 + \frac{- 2 p}{3}$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

Step 2.2.3.1.3

Move the negative in front of the fraction.

$r = 0.58 - \frac{2 p}{3}$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

$r = 0.58 - \frac{2 p}{3}$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

$r = 0.58 - \frac{2 p}{3}$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

$r = 0.58 - \frac{2 p}{3}$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

$r = 0.58 - \frac{2 p}{3}$

$x = 10 r + 50 p$

$20 r + 12 p = 11.04$

Step 3

Replace all occurrences of $r$ with $0.58 - \frac{2 p}{3}$ in each equation.

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Step 3.1

Replace all occurrences of $r$ in $x = 10 r + 50 p$ with $0.58 - \frac{2 p}{3}$ .

$x = 10 (0.58 - \frac{2 p}{3}) + 50 p$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $10 (0.58 - \frac{2 p}{3}) + 50 p$ .

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Step 3.2.1.1

Simplify each term.

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Step 3.2.1.1.1

Apply the distributive property.

$x = 10 \cdot 0.58 + 10 (- \frac{2 p}{3}) + 50 p$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

Step 3.2.1.1.2

Multiply $10$ by $0.58$ .

$x = 5.8 + 10 (- \frac{2 p}{3}) + 50 p$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

Step 3.2.1.1.3

Multiply $10 (- \frac{2 p}{3})$ .

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Step 3.2.1.1.3.1

Multiply $- 1$ by $10$ .

$x = 5.8 - 10 \frac{2 p}{3} + 50 p$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

Step 3.2.1.1.3.2

Combine $- 10$ and $\frac{2 p}{3}$ .

$x = 5.8 + \frac{- 10 (2 p)}{3} + 50 p$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

Step 3.2.1.1.3.3

Multiply $2$ by $- 10$ .

$x = 5.8 + \frac{- 20 p}{3} + 50 p$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

$x = 5.8 + \frac{- 20 p}{3} + 50 p$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

Step 3.2.1.1.4

Move the negative in front of the fraction.

$x = 5.8 - \frac{20 p}{3} + 50 p$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

$x = 5.8 - \frac{20 p}{3} + 50 p$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

Step 3.2.1.2

To write $50 p$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = 5.8 - \frac{20 p}{3} + 50 p \cdot \frac{3}{3}$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

Step 3.2.1.3

Simplify terms.

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Step 3.2.1.3.1

Combine $50 p$ and $\frac{3}{3}$ .

$x = 5.8 - \frac{20 p}{3} + \frac{50 p \cdot 3}{3}$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

Step 3.2.1.3.2

Combine the numerators over the common denominator.

$x = 5.8 + \frac{- 20 p + 50 p \cdot 3}{3}$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

$x = 5.8 + \frac{- 20 p + 50 p \cdot 3}{3}$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

Step 3.2.1.4

Simplify the numerator.

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Step 3.2.1.4.1

Factor $10 p$ out of $- 20 p + 50 p \cdot 3$ .

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Step 3.2.1.4.1.1

Factor $10 p$ out of $- 20 p$ .

$x = 5.8 + \frac{10 p (- 2) + 50 p \cdot 3}{3}$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

Step 3.2.1.4.1.2

Factor $10 p$ out of $50 p \cdot 3$ .

$x = 5.8 + \frac{10 p (- 2) + 10 p (5 \cdot 3)}{3}$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

Step 3.2.1.4.1.3

Factor $10 p$ out of $10 p (- 2) + 10 p (5 \cdot 3)$ .

$x = 5.8 + \frac{10 p (- 2 + 5 \cdot 3)}{3}$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

$x = 5.8 + \frac{10 p (- 2 + 5 \cdot 3)}{3}$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

Step 3.2.1.4.2

Multiply $5$ by $3$ .

$x = 5.8 + \frac{10 p (- 2 + 15)}{3}$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

Step 3.2.1.4.3

Add $- 2$ and $15$ .

$x = 5.8 + \frac{10 p \cdot 13}{3}$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

Step 3.2.1.4.4

Multiply $13$ by $10$ .

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$20 r + 12 p = 11.04$

Step 3.3

Replace all occurrences of $r$ in $20 r + 12 p = 11.04$ with $0.58 - \frac{2 p}{3}$ .

$20 (0.58 - \frac{2 p}{3}) + 12 p = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 3.4

Simplify the left side.

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Step 3.4.1

Simplify $20 (0.58 - \frac{2 p}{3}) + 12 p$ .

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Step 3.4.1.1

Simplify each term.

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Step 3.4.1.1.1

Apply the distributive property.

$20 \cdot 0.58 + 20 (- \frac{2 p}{3}) + 12 p = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 3.4.1.1.2

Multiply $20$ by $0.58$ .

$11.6 + 20 (- \frac{2 p}{3}) + 12 p = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 3.4.1.1.3

Multiply $20 (- \frac{2 p}{3})$ .

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Step 3.4.1.1.3.1

Multiply $- 1$ by $20$ .

$11.6 - 20 \frac{2 p}{3} + 12 p = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 3.4.1.1.3.2

Combine $- 20$ and $\frac{2 p}{3}$ .

$11.6 + \frac{- 20 (2 p)}{3} + 12 p = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 3.4.1.1.3.3

Multiply $2$ by $- 20$ .

$11.6 + \frac{- 40 p}{3} + 12 p = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$11.6 + \frac{- 40 p}{3} + 12 p = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 3.4.1.1.4

Move the negative in front of the fraction.

$11.6 - \frac{40 p}{3} + 12 p = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$11.6 - \frac{40 p}{3} + 12 p = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 3.4.1.2

To write $12 p$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$11.6 - \frac{40 p}{3} + 12 p \cdot \frac{3}{3} = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 3.4.1.3

Simplify terms.

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Step 3.4.1.3.1

Combine $12 p$ and $\frac{3}{3}$ .

$11.6 - \frac{40 p}{3} + \frac{12 p \cdot 3}{3} = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 3.4.1.3.2

Combine the numerators over the common denominator.

$11.6 + \frac{- 40 p + 12 p \cdot 3}{3} = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$11.6 + \frac{- 40 p + 12 p \cdot 3}{3} = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 3.4.1.4

Simplify each term.

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Step 3.4.1.4.1

Simplify the numerator.

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Step 3.4.1.4.1.1

Factor $4 p$ out of $- 40 p + 12 p \cdot 3$ .

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Step 3.4.1.4.1.1.1

Factor $4 p$ out of $- 40 p$ .

$11.6 + \frac{4 p (- 10) + 12 p \cdot 3}{3} = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 3.4.1.4.1.1.2

Factor $4 p$ out of $12 p \cdot 3$ .

$11.6 + \frac{4 p (- 10) + 4 p (3 \cdot 3)}{3} = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 3.4.1.4.1.1.3

Factor $4 p$ out of $4 p (- 10) + 4 p (3 \cdot 3)$ .

$11.6 + \frac{4 p (- 10 + 3 \cdot 3)}{3} = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$11.6 + \frac{4 p (- 10 + 3 \cdot 3)}{3} = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 3.4.1.4.1.2

Multiply $3$ by $3$ .

$11.6 + \frac{4 p (- 10 + 9)}{3} = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 3.4.1.4.1.3

Add $- 10$ and $9$ .

$11.6 + \frac{4 p \cdot - 1}{3} = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 3.4.1.4.1.4

Multiply $- 1$ by $4$ .

$11.6 + \frac{- 4 p}{3} = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$11.6 + \frac{- 4 p}{3} = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 3.4.1.4.2

Move the negative in front of the fraction.

$11.6 - \frac{4 p}{3} = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$11.6 - \frac{4 p}{3} = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$11.6 - \frac{4 p}{3} = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$11.6 - \frac{4 p}{3} = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$11.6 - \frac{4 p}{3} = 11.04$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 4

Solve for $p$ in $11.6 - \frac{4 p}{3} = 11.04$ .

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Step 4.1

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

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Step 4.1.1

Subtract $11.6$ from both sides of the equation.

$- \frac{4 p}{3} = 11.04 - 11.6$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 4.1.2

Subtract $11.6$ from $11.04$ .

$- \frac{4 p}{3} = - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$- \frac{4 p}{3} = - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 4.2

Multiply both sides of the equation by $- \frac{3}{4}$ .

$- \frac{3}{4} \cdot (- \frac{4 p}{3}) = - \frac{3}{4} \cdot - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 4.3

Simplify both sides of the equation.

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Step 4.3.1

Simplify the left side.

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Step 4.3.1.1

Simplify $- \frac{3}{4} (- \frac{4 p}{3})$ .

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Step 4.3.1.1.1

Cancel the common factor of $3$ .

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Step 4.3.1.1.1.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} \cdot (- \frac{4 p}{3}) = - \frac{3}{4} \cdot - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 4.3.1.1.1.2

Move the leading negative in $- \frac{4 p}{3}$ into the numerator.

$\frac{- 3}{4} \cdot \frac{- 4 p}{3} = - \frac{3}{4} \cdot - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 4.3.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{4} \cdot \frac{- 4 p}{3} = - \frac{3}{4} \cdot - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 4.3.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{4} \cdot \frac{- 4 p}{3} = - \frac{3}{4} \cdot - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 4.3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{4} \cdot (- 4 p) = - \frac{3}{4} \cdot - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$\frac{- 1}{4} \cdot (- 4 p) = - \frac{3}{4} \cdot - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 4.3.1.1.2

Cancel the common factor of $4$ .

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Step 4.3.1.1.2.1

Factor $4$ out of $- 4 p$ .

$\frac{- 1}{4} \cdot (4 (- p)) = - \frac{3}{4} \cdot - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 4.3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{4} \cdot (4 (- p)) = - \frac{3}{4} \cdot - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 4.3.1.1.2.3

Rewrite the expression.

$p = - \frac{3}{4} \cdot - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$p = - \frac{3}{4} \cdot - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 4.3.1.1.3

Multiply.

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Step 4.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 p = - \frac{3}{4} \cdot - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 4.3.1.1.3.2

Multiply $p$ by $1$ .

$p = - \frac{3}{4} \cdot - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$p = - \frac{3}{4} \cdot - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$p = - \frac{3}{4} \cdot - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$p = - \frac{3}{4} \cdot - 0.56$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 4.3.2

Simplify the right side.

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Step 4.3.2.1

Simplify $- \frac{3}{4} \cdot - 0.56$ .

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Step 4.3.2.1.1

Multiply $- \frac{3}{4} \cdot - 0.56$ .

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Step 4.3.2.1.1.1

Multiply $- 0.56$ by $- 1$ .

$p = 0.56 (\frac{3}{4})$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 4.3.2.1.1.2

Combine $0.56$ and $\frac{3}{4}$ .

$p = \frac{0.56 \cdot 3}{4}$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 4.3.2.1.1.3

Multiply $0.56$ by $3$ .

$p = \frac{1.68}{4}$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$p = \frac{1.68}{4}$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 4.3.2.1.2

Divide $1.68$ by $4$ .

$p = 0.42$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$p = 0.42$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$p = 0.42$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$p = 0.42$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

$p = 0.42$

$x = 5.8 + \frac{130 p}{3}$

$r = 0.58 - \frac{2 p}{3}$

Step 5

Replace all occurrences of $p$ with $0.42$ in each equation.

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Step 5.1

Replace all occurrences of $p$ in $x = 5.8 + \frac{130 p}{3}$ with $0.42$ .

$x = 5.8 + \frac{130 (0.42)}{3}$

$p = 0.42$

$r = 0.58 - \frac{2 p}{3}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $5.8 + \frac{130 (0.42)}{3}$ .

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Step 5.2.1.1

Multiply $130$ by $0.42$ .

$x = 5.8 + \frac{54.6}{3}$

$p = 0.42$

$r = 0.58 - \frac{2 p}{3}$

Step 5.2.1.2

Divide $54.6$ by $3$ .

$x = 5.8 + 18.2$

$p = 0.42$

$r = 0.58 - \frac{2 p}{3}$

Step 5.2.1.3

Add $5.8$ and $18.2$ .

$x = 24$

$p = 0.42$

$r = 0.58 - \frac{2 p}{3}$

$x = 24$

$p = 0.42$

$r = 0.58 - \frac{2 p}{3}$

$x = 24$

$p = 0.42$

$r = 0.58 - \frac{2 p}{3}$

Step 5.3

Replace all occurrences of $p$ in $r = 0.58 - \frac{2 p}{3}$ with $0.42$ .

$r = 0.58 - \frac{2 (0.42)}{3}$

$x = 24$

$p = 0.42$

Step 5.4

Simplify the right side.

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Step 5.4.1

Simplify $0.58 - \frac{2 (0.42)}{3}$ .

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Step 5.4.1.1

Simplify each term.

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Step 5.4.1.1.1

Multiply $2$ by $0.42$ .

$r = 0.58 - \frac{0.84}{3}$

$x = 24$

$p = 0.42$

Step 5.4.1.1.2

Divide $0.84$ by $3$ .

$r = 0.58 - 1 \cdot 0.28$

$x = 24$

$p = 0.42$

Step 5.4.1.1.3

Multiply $- 1$ by $0.28$ .

$r = 0.58 - 0.28$

$x = 24$

$p = 0.42$

$r = 0.58 - 0.28$

$x = 24$

$p = 0.42$

Step 5.4.1.2

Subtract $0.28$ from $0.58$ .

$r = 0.3$

$x = 24$

$p = 0.42$

$r = 0.3$

$x = 24$

$p = 0.42$

$r = 0.3$

$x = 24$

$p = 0.42$

$r = 0.3$

$x = 24$

$p = 0.42$

Step 6

List all of the solutions.

$r = 0.3, x = 24, p = 0.42$