Q: How do you solve percent problems using proportions?
A: Generally, there are 3 main parts to a percent problem: the percent, the part and the total.
The set up is the same for all problems:
part/total = percent/100
(remember, percent means per 100, so it is always out of 100)
Example 1: Finding the percent:
What percent is 75 of 85?
Set-up
75/85 = x/100
Cross multiply:
75*100 = 85*x
7500 = 85x
7500/85 = x
88.235% = x
So, 75 is 88.235% of the number 85.
Example 2: Finding the “part”:
What is 76% of 50?
Set-up
x/50 = 76/100
Cross multiply:
100x = 76*50
100x = 3800
x = 3800/100
x = 38
So, 76% of 50 is 38.
Example 3: Finding the “total”:
60 is 24% of what number?
Set-up
60/x = 24/100
Cross multiply:
24x = 60*100
24x = 6000
x = 6000/24
x = 250
So, 60 is 24% of the number 250.