Finite Math Examples

$5000 = 5525 (1 + (3) r)$

Step 1

Rewrite the equation as $5525 (1 + 3 r) = 5000$ .

$5525 (1 + 3 r) = 5000$

Step 2

Divide each term in $5525 (1 + 3 r) = 5000$ by $5525$ and simplify.

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Step 2.1

Divide each term in $5525 (1 + 3 r) = 5000$ by $5525$ .

$\frac{5525 (1 + 3 r)}{5525} = \frac{5000}{5525}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5525$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5525 (1 + 3 r)}{5525} = \frac{5000}{5525}$

Step 2.2.1.2

Divide $1 + 3 r$ by $1$ .

$1 + 3 r = \frac{5000}{5525}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $5000$ and $5525$ .

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Step 2.3.1.1

Factor $25$ out of $5000$ .

$1 + 3 r = \frac{25 (200)}{5525}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $25$ out of $5525$ .

$1 + 3 r = \frac{25 \cdot 200}{25 \cdot 221}$

Step 2.3.1.2.2

Cancel the common factor.

$1 + 3 r = \frac{25 \cdot 200}{25 \cdot 221}$

Step 2.3.1.2.3

Rewrite the expression.

$1 + 3 r = \frac{200}{221}$

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.

$3 r = \frac{200}{221} - 1$

Step 3.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{221}{221}$ .

$3 r = \frac{200}{221} - 1 \cdot \frac{221}{221}$

Step 3.3

Combine $- 1$ and $\frac{221}{221}$ .

$3 r = \frac{200}{221} + \frac{- 1 \cdot 221}{221}$

Step 3.4

Combine the numerators over the common denominator.

$3 r = \frac{200 - 1 \cdot 221}{221}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 1$ by $221$ .

$3 r = \frac{200 - 221}{221}$

Step 3.5.2

Subtract $221$ from $200$ .

$3 r = \frac{- 21}{221}$

Step 3.6

Move the negative in front of the fraction.

$3 r = - \frac{21}{221}$

Step 4

Divide each term in $3 r = - \frac{21}{221}$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 r = - \frac{21}{221}$ by $3$ .

$\frac{3 r}{3} = \frac{- \frac{21}{221}}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 r}{3} = \frac{- \frac{21}{221}}{3}$

Step 4.2.1.2

Divide $r$ by $1$ .

$r = \frac{- \frac{21}{221}}{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$r = - \frac{21}{221} \cdot \frac{1}{3}$

Step 4.3.2

Cancel the common factor of $3$ .

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Step 4.3.2.1

Move the leading negative in $- \frac{21}{221}$ into the numerator.

$r = \frac{- 21}{221} \cdot \frac{1}{3}$

Step 4.3.2.2

Factor $3$ out of $- 21$ .

$r = \frac{3 (- 7)}{221} \cdot \frac{1}{3}$

Step 4.3.2.3

Cancel the common factor.

$r = \frac{3 \cdot - 7}{221} \cdot \frac{1}{3}$

Step 4.3.2.4

Rewrite the expression.

$r = \frac{- 7}{221}$

Step 4.3.3

Move the negative in front of the fraction.

$r = - \frac{7}{221}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$r = - \frac{7}{221}$

Decimal Form:

$r = - 0.03167420 \dots$