Finite Math Examples

$22$ , $135 = 19000 (1 + r (39))$

Step 1

Rewrite the equation as $19000 (1 + r (39)) = 135$ .

$19000 (1 + r (39)) = 135$

Step 2

Divide each term in $19000 (1 + r (39)) = 135$ by $19000$ and simplify.

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Step 2.1

Divide each term in $19000 (1 + r (39)) = 135$ by $19000$ .

$\frac{19000 (1 + r (39))}{19000} = \frac{135}{19000}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $19000$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{19000 (1 + r (39))}{19000} = \frac{135}{19000}$

Step 2.2.1.2

Divide $1 + r (39)$ by $1$ .

$1 + r (39) = \frac{135}{19000}$

Step 2.2.2

Move $39$ to the left of $r$ .

$1 + 39 r = \frac{135}{19000}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $135$ and $19000$ .

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Step 2.3.1.1

Factor $5$ out of $135$ .

$1 + 39 r = \frac{5 (27)}{19000}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $5$ out of $19000$ .

$1 + 39 r = \frac{5 \cdot 27}{5 \cdot 3800}$

Step 2.3.1.2.2

Cancel the common factor.

$1 + 39 r = \frac{5 \cdot 27}{5 \cdot 3800}$

Step 2.3.1.2.3

Rewrite the expression.

$1 + 39 r = \frac{27}{3800}$

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.

$39 r = \frac{27}{3800} - 1$

Step 3.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3800}{3800}$ .

$39 r = \frac{27}{3800} - 1 \cdot \frac{3800}{3800}$

Step 3.3

Combine $- 1$ and $\frac{3800}{3800}$ .

$39 r = \frac{27}{3800} + \frac{- 1 \cdot 3800}{3800}$

Step 3.4

Combine the numerators over the common denominator.

$39 r = \frac{27 - 1 \cdot 3800}{3800}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 1$ by $3800$ .

$39 r = \frac{27 - 3800}{3800}$

Step 3.5.2

Subtract $3800$ from $27$ .

$39 r = \frac{- 3773}{3800}$

Step 3.6

Move the negative in front of the fraction.

$39 r = - \frac{3773}{3800}$

Step 4

Divide each term in $39 r = - \frac{3773}{3800}$ by $39$ and simplify.

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Step 4.1

Divide each term in $39 r = - \frac{3773}{3800}$ by $39$ .

$\frac{39 r}{39} = \frac{- \frac{3773}{3800}}{39}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $39$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{39 r}{39} = \frac{- \frac{3773}{3800}}{39}$

Step 4.2.1.2

Divide $r$ by $1$ .

$r = \frac{- \frac{3773}{3800}}{39}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$r = - \frac{3773}{3800} \cdot \frac{1}{39}$

Step 4.3.2

Multiply $- \frac{3773}{3800} \cdot \frac{1}{39}$ .

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Step 4.3.2.1

Multiply $\frac{1}{39}$ by $\frac{3773}{3800}$ .

$r = - \frac{3773}{39 \cdot 3800}$

Step 4.3.2.2

Multiply $39$ by $3800$ .

$r = - \frac{3773}{148200}$

Step 5

Replace the variable $r$ with $- \frac{3773}{148200}$ in the expression.

$22$