Word Problems Involving Percent
Three Kinds of Percent Problems
Consider the statement " percent of is ."
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 is the unknown (e.g. "What percent of is ?")
problems where is the unknown (e.g. " is of what number?")
problems where is the unknown (e.g. "What is of ?")
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 seats, of which are occupied. Express the attendance at a percent of capacity.
The question here can be stated as, "What percent of is ?" So, the unknown here is .
Write a proportion.
You could cross multiply. Or, you could notice that the denominator on the left is times the denominator on the right.
So, to find , just divide the numerator on the left by .
So, the hall is filled to capacity.
Example 2:
of the earth's surface--that's about 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, " percent of what number is ?" So, the unknown here is .
Write a proportion.
Cross multiply.
Divide both sides by .
So, the earth's surface area is about square kilometers.
Example 3:
The residents of a state were surveyed about their opinion of the public education system. said "Good", said "Bad", and the rest said "No opinion".
If people were surveyed, how many said "No opinion"?
The total of the three percentages should be . Find the percentage of people who said "No opinion."
The question here can be stated as, "What is of ?" So, the unknown here is .
Write a proportion.
Cross multiply.
So, people said "No opinion".