Finite Math Examples

$5022.5 = 4900 (1 + (r) (\frac{1}{2}))$

Step 1

Rewrite the equation as $4900 (1 + r (\frac{1}{2})) = 5022.5$ .

$4900 (1 + r (\frac{1}{2})) = 5022.5$

Step 2

Simplify $4900 (1 + r (\frac{1}{2}))$ .

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Step 2.1

Combine $r$ and $\frac{1}{2}$ .

$4900 (1 + \frac{r}{2}) = 5022.5$

Step 2.2

Apply the distributive property.

$4900 \cdot 1 + 4900 \frac{r}{2} = 5022.5$

Step 2.3

Multiply $4900$ by $1$ .

$4900 + 4900 \frac{r}{2} = 5022.5$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Factor $2$ out of $4900$ .

$4900 + 2 (2450) \frac{r}{2} = 5022.5$

Step 2.4.2

Cancel the common factor.

$4900 + 2 \cdot 2450 \frac{r}{2} = 5022.5$

Step 2.4.3

Rewrite the expression.

$4900 + 2450 r = 5022.5$

Step 3

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

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Step 3.1

Subtract $4900$ from both sides of the equation.

$2450 r = 5022.5 - 4900$

Step 3.2

Subtract $4900$ from $5022.5$ .

$2450 r = 122.5$

Step 4

Divide each term in $2450 r = 122.5$ by $2450$ and simplify.

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Step 4.1

Divide each term in $2450 r = 122.5$ by $2450$ .

$\frac{2450 r}{2450} = \frac{122.5}{2450}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2450$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2450 r}{2450} = \frac{122.5}{2450}$

Step 4.2.1.2

Divide $r$ by $1$ .

$r = \frac{122.5}{2450}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $122.5$ by $2450$ .

$r = 0.05$