Percent Problems: Proportion Method - Alamo Colleges District
Math 0300
Percent Problems: Proportion Method
To solve percent problems using proportions
Problems that can be solved using the basic percent equation can also be solved using proportions.
The proportion method is based on writing two ratios. One ratio is the percent ratio,
percent
amount
written as 100 . The second ratio is the amount-to-base ratio, written as base .
These two ratios form the proportion:
percent 100
=
amount base
To use the proportion method, first identify the percent, the amount, and the Base (the base usually follows the phrase "percent of").
Example 1: What is 23 % of 45?
23 = n 100 45
23(45) = 100n
1035 = 100n
1035 = 100n 100 100
10.35 = n
Example 2: What percent of 25 is 4? n =4
100 25
25n = 100(4)
25n = 400
25n = 400 = n = 16% 25 25
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Math 0300
Example 3: 12 is 60% of what number?
60 100
=
12 n
60n = 100 (12)
60n = 1200 60n = 1200 60 60
n = 20
To solve application problems
Example 4: An antiques dealer found that 86 % of the 250 items that were sold for under $1000. How many items sold for under $1,000?
Strategy To find the number of items that sold for under $1000, write and solve a proportion, using n to represent the number of items sold (amount) for less than $1000. The percent is 86% and the base is 250.
Solution 86 = n 100 250
86(250) = 100n
21,500 = 100n
21,500 = 100n 100 100
215 = n
215 items sold for under $1,000.
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