# AYSO has 18 8th grade boys’ teams this year, but this is a 28% (rounded to the nearest whole number) decrease from the prior year. How many 8th grade teams were there last year?

Jun 23, 2018

See a solution process below:

#### Explanation:

The formula for calculating the percent change in a value between two points in time is:

$p = \frac{N - O}{O} \cdot 100$

Where:

$p$ is the percent change - -28% for this problem.

$N$ is the New Value - 18 in this problem.

$O$ is the Old Value - what we are solving for in this problem.

Substituting and solving for $O$ gives:

$- 28 = \frac{18 - O}{O} \cdot 100$

$- 28 = \left(\frac{18}{O} - \frac{O}{O}\right) \cdot 100$

$- 28 = \left(\frac{18}{O} - 1\right) \cdot 100$

$- 28 = \left(\frac{18}{O} \cdot 100\right) - \left(1 \cdot 100\right)$

$- 28 = \frac{1800}{O} - 100$

$- 28 + \textcolor{red}{100} = \frac{1800}{O} - 100 + \textcolor{red}{100}$

$72 = \frac{1800}{O} - 0$

$72 = \frac{1800}{O}$

$\frac{\textcolor{red}{O}}{\textcolor{b l u e}{72}} \times 72 = \frac{\textcolor{red}{O}}{\textcolor{b l u e}{72}} \times \frac{1800}{O}$

$\frac{\textcolor{red}{O}}{\cancel{\textcolor{b l u e}{72}}} \times \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{72}}} = \frac{\cancel{\textcolor{red}{O}}}{\textcolor{b l u e}{72}} \times \frac{1800}{\textcolor{red}{\cancel{\textcolor{b l a c k}{O}}}}$

$O = \frac{1800}{\textcolor{b l u e}{72}}$

$O = 25$

Last year there were $\textcolor{red}{25}$ 8th grade Teams