Print-friendly page

Basic "Percent of" Word Problems (page 1 of 3)

Sections: Basic percentage exercises, Markup / markdown, General increase / decrease

When you learned how to translate simple English statements into mathematical expressions, you learned that "of" can indicate "times". This frequently comes up when using percentages.

If you need to find 16% of 1400, you first convert the percentage "16%" to the number "0.16". (Remember: When you are doing actual math, you need to use actual numbers. Always convert the percentages to decimals!) Then, since "sixteen percent OF fourteen hundred" tells you to multiply the 0.16 and the 1400, you get: (0.16)(1400) = 224. This says that 224 is sixteen percent of 1400.

Percentage problems usually work off of some version of the sentence "(this) is (some percentage) of (that)", which translates to "(this) = (some percentage) × (that)". You will be given two of the values (or enough information that you can figure two of them out), and then you'll need to pick a variable for the value you don't have, write an equation, and solve for that variable. Here are some more examples:

• What percent of 20 is 30?

We have the original number (20) and the comparative number (30). The unknown in this problem is the rate. Since the statement is "(thirty) is (some percentage) of (twenty)", then the variable stands for the percentage, and the equation is:

30 = (x)(20)

30/20 = x = 1.5

Since x stands for a percentage, I need to remember to convert this decimal back into a percentage:

1.5 = 150%

Thirty is 150% of 20.

• What is 35% of 80?

Here we have the rate (35%) and the original number (80); the unknown is the comparative number that is 35% of 80. Since this statement is "(some number) is (thirty-five percent) of (eighty)", then the variable stands for a number and the equation is:

x = (0.35)(80)

x = 28

Twenty-eight is 35% of 80.

• 45% of what is 9?

Here we have the rate (45%) and the comparative number (9); the unknown is the original number that 9 is 45% of. The statement is "(nine) is (forty-five percent) of (some number)", so the variable stands for a number, and the equation is:

9 = (0.45)(x)

⁹/_0.45 = x = 20

Nine is 45% of 20.

Note the construction of each of the above sentences: (this number) is (some percent) of (that number).  This format always holds true for percents. In any given problem, you plug your known values into this equation, and solve for whatever is left. For example:

• Suppose you bought something that was priced at $6.95, and the total bill was $7.61. What is the sales tax rate in this city? (Round answer to one decimal place.)

The sales tax is a certain percentage of the price, so we first have to figure what the actual tax was. The tax was:

7.61 – 6.95 = 0.66

Then (the sales tax) is (some percentage) of (the price), or, in mathematical terms:

0.66 = (x)(6.95)

Solving for x, I get:

^0.66/_6.95 = x = 0.094964028... = 9.4964028...%

The sales tax rate is 9.5%.

In the above example, we first had to figure out what the actual tax was. Many percentage problems are really "two-part-ers" like this: they involve some kind of increase or decrease relative to some original value. Note that we always figure the percentage of change relative to the original value! For instance:

• Suppose a certain item used to sell for seventy-five cents a pound, you see that it's been marked up to eighty-one cents a pound. What is the percent increase?

First, I have to find the absolute increase:   Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

81 – 75 = 6

The price has gone up six cents. Now I can find the percentage increase over the original price. (Note this language, "increase/decrease over the original", and use it to your advantage: it will remind you to put the increase or decrease over the original, and divide.) This percentage increase is the relative change:

⁶/₇₅ = 0.08

...or an 8% increase in price per pound.

Top  |  1 | 2 | 3  |  Return to Index  Next >>

  Copyright © 2006-2008  Elizabeth Stapel   |   About   |   Terms of Use

 Feedback   |   Error?