# An item that was $1,525 is now $1,708. What was the percent change?

Jan 4, 2017

The percent increase in price was 12%.

#### Explanation:

We first determine the difference in price as

$1708 - 1525 = 183$

To determine the percent change, we write:

$1525 \times \frac{x}{100} = 183$

Reduce the left side by dividing the numerator and denominator by $5$ progressively.

$305 \cancel{1525} \times \frac{x}{20 \cancel{100}} = 183$

$61 \cancel{305} \times \frac{x}{4 \cancel{20}} = 183$

Divide both sides by $61$.

$\frac{x}{4} = \frac{183}{61}$

$\frac{x}{4} = \frac{3 \times 61}{61}$

$\frac{x}{4} = 3 \times \frac{\cancel{61}}{\cancel{61}}$

$\frac{x}{4} = 3$

Multiply both sides by $4$.

$x = 12$