Finite Math Examples

$4660.9 = 2912.09 (1 + \frac{7}{13} r)$

Step 1

Rewrite the equation as $2912.09 (1 + \frac{7}{13} r) = 4660.9$ .

$2912.09 (1 + \frac{7}{13} r) = 4660.9$

Step 2

Divide each term in $2912.09 (1 + \frac{7}{13} r) = 4660.9$ by $2912.09$ and simplify.

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Step 2.1

Divide each term in $2912.09 (1 + \frac{7}{13} r) = 4660.9$ by $2912.09$ .

$\frac{2912.09 (1 + \frac{7}{13} r)}{2912.09} = \frac{4660.9}{2912.09}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2912.09$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2912.09 (1 + \frac{7}{13} r)}{2912.09} = \frac{4660.9}{2912.09}$

Step 2.2.1.2

Divide $1 + \frac{7}{13} r$ by $1$ .

$1 + \frac{7}{13} r = \frac{4660.9}{2912.09}$

Step 2.2.2

Combine $\frac{7}{13}$ and $r$ .

$1 + \frac{7 r}{13} = \frac{4660.9}{2912.09}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $4660.9$ by $2912.09$ .

$1 + \frac{7 r}{13} = 1.60053432$

Step 3

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

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Step 3.1

Subtract $1$ from both sides of the equation.

$\frac{7 r}{13} = 1.60053432 - 1$

Step 3.2

Subtract $1$ from $1.60053432$ .

$\frac{7 r}{13} = 0.60053432$

Step 4

Multiply both sides of the equation by $\frac{13}{7}$ .

$\frac{13}{7} \cdot \frac{7 r}{13} = \frac{13}{7} \cdot 0.60053432$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{13}{7} \cdot \frac{7 r}{13}$ .

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Step 5.1.1.1

Cancel the common factor of $13$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{13}{7} \cdot \frac{7 r}{13} = \frac{13}{7} \cdot 0.60053432$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 r) = \frac{13}{7} \cdot 0.60053432$

Step 5.1.1.2

Cancel the common factor of $7$ .

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Step 5.1.1.2.1

Factor $7$ out of $7 r$ .

$\frac{1}{7} (7 (r)) = \frac{13}{7} \cdot 0.60053432$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 r) = \frac{13}{7} \cdot 0.60053432$

Step 5.1.1.2.3

Rewrite the expression.

$r = \frac{13}{7} \cdot 0.60053432$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{13}{7} \cdot 0.60053432$ .

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Step 5.2.1.1

Multiply $\frac{13}{7} \cdot 0.60053432$ .

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Step 5.2.1.1.1

Combine $\frac{13}{7}$ and $0.60053432$ .

$r = \frac{13 \cdot 0.60053432}{7}$

Step 5.2.1.1.2

Multiply $13$ by $0.60053432$ .

$r = \frac{7.80694621}{7}$

Step 5.2.1.2

Divide $7.80694621$ by $7$ .

$r = 1.11527803$