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Solving Percent Problems using Proportions

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.

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