# Suresh played 80 hours of tennis last week. This week Suresh played 50% less tennis. How many hours of tennis did Suresh play this week?

Mar 7, 2017

Suresh played 40 hours of tennis this week

#### Explanation:

The formula for determining the percentage change or rate of change is:

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

$p$ is the percentage change: -50 for this problem
$N$ is the New Value: what we will solve for in this problem
$O$ is the Old Value: 80 hours for this problem

Substituting and solving for $N$ gives:

$- 50 = \frac{N - 80}{80} \cdot 100$

$\frac{\textcolor{b l u e}{80}}{\textcolor{red}{100}} \times - 50 = \frac{\textcolor{b l u e}{80}}{\textcolor{red}{100}} \times \frac{N - 80}{80} \cdot 100$

$- \frac{4000}{\textcolor{red}{100}} = \frac{\cancel{\textcolor{b l u e}{80}}}{\cancel{\textcolor{red}{100}}} \times \frac{N - 80}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{80}}}} \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{100}}}$

$- 40 = N - 80$

$- 40 + \textcolor{red}{80} = N - 80 + \textcolor{red}{80}$

$40 = N - 0$

$40 = N$

$N = 40$