# How do you find the percent change given the original number is 50 and new number is 30?

Jan 20, 2017

See the solution process below:

#### Explanation:

The formula for calculating the rate or percentage change is:

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

Where:

$p$ is the percentage change
$N$ is the New Value (30 in this case)
$O$ is the Old Value (50 in this case)

Substituting and solving for $p$ gives:

$p = \frac{30 - 50}{50} \cdot 100$

$p = \frac{- 20}{50} \cdot 100$

$p = \frac{- 2000}{50}$

$p = - 40$

The percentage change is -40%#