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Word Problems Involving Percent

Three Kinds of Percent Problems

Consider the statement " x percent of y is z ."

If any two of the variables are given, you can use algebra to find out the missing one. This results in three different kinds of problems. In each one, the unknown is in a different position.

•  problems where x is the unknown (e.g. "What percent of 44 is 11 ?")

•  problems where y is the unknown (e.g. " 58 is 25 % of what number?")

•  problems where z is the unknown (e.g. "What is 88 % of 5000 ?")

When given a word problem involving percents, then, the first job is to find out what the unknown is.

 

Example 1:

A concert hall has 400 seats, of which 325 are occupied. Express the attendance at a percent of capacity.

The question here can be stated as, "What percent of 400 is 325 ?" So, the unknown here is x .

Write a proportion.

325 400 = x 100

You could cross multiply. Or, you could notice that the denominator on the left is 4 times the denominator on the right.

So, to find x , just divide the numerator on the left by 4 .

x = 325 4 = 81.25

So, the hall is filled to 81.25 % capacity.

Example 2:

71 % of the earth's surface--that's about 362,100,000 square kilometers--is covered by water. Use this information to find the total surface area of the earth.

The question here can be stated as, " 71 % percent of what number is 362,100,000 ?" So, the unknown here is y .

Write a proportion.

362 , 100 , 000 y = 71 100

Cross multiply.

71 y = 36 , 210 , 000 , 000

Divide both sides by 71 .

y = 510 , 000 , 000

So, the earth's surface area is about 510,000,000 square kilometers.

Example 3:

The residents of a state were surveyed about their opinion of the public education system. 12 % said "Good", 54 % said "Bad", and the rest said "No opinion".

If 650 people were surveyed, how many said "No opinion"?

The total of the three percentages should be 100 . Find the percentage of people who said "No opinion."

12 + 54 + c = 100 66 + c = 100 c = 34

The question here can be stated as, "What is 34 % of 650 ?" So, the unknown here is z .

Write a proportion.

z 650 = 34 100

Cross multiply.

100 z = 22100 z = 221

So, 221 people said "No opinion".