Percent of Increase, Decrease, Discount
There are many situations that involve increasing or decreasing an amount by a certain percent. Check out the following examples:
Example 1. You normally work at the mall over the spring break for $450. This year the boss tells you that you will be receiving a 7% raise. How much of an increase will you be receiving? How much will you be earning in total this year?
Solution: Your raise is 7% of your old salary.
Let r = your raise
r = 7% × 450
r = 0.07 × 450 changing 7% to a decimal
r = 31.5
Your raise will be $31.50.
Your total earnings will be $450 + $31.50
which equals $481.50.
Example 2. Your dream CD player is on sale for 20% off the original price. If the original price is $270, what is the sale price?
Solution: First, we will find the amount of the discount.
The discount = 20% of original price.
Let x = the discount.
x = 20% × 270
x = 0.20 × 270
x = 54
The discount is $54.
Now, the sale price will be $270 – $54
which equals $216 for the sale price.
Example 3. The enrollment at a local elementary school had 560 students last year. This year the enrollment has decreased by 48 students. What is the percent of decrease to the nearest tenth of a percent?
Solution: The enrollment decrease = the percent of decrease of 560.
percent of decrease = \(\frac { 48 }{ 560 } \) × 100
= 8.57 %
