Basic Mathematics for College Students

Percent sentences involve a comparison of numbers. In the statement “420 is 84%
of 500,” the number 420 is called the amount,84% is the percent,and 500 is called the
base.Think of the base as the standard of comparison—it represents the wholeof
some quantity. The amount is a partof the base, but it can exceed the base when the
percent is more than 100%. The percent, of course, has the % symbol.

is of

Amount percent base
(part) (whole)
In any percent problem, the relationship between the amount, the percent, and
the base is as follows:Amount is percent of base.This relationship is shown below as
the percent equation (also called the percent formula).

42 84% 500.

6.2 Solving Percent Problems Using Percent Equations and Proportions 515

Caution! When solving percent equations, always write the percent as a

decimal (or a fraction) before performing any calculations. In Example 2, we

wrote 84% as 0.84 before multiplying by 500.

Percent Equation (Formula)

Any percent sentence can be translated to a percent equation that has the

form:

Amount percent base or Part percent whole

EXAMPLE (^3) What number is 160% of 15.8?
StrategyWe will look for the key words is, of,and what numberin the percent
sentence and translate them to mathematical symbols to form a percent equation.
WHYThen it will be clear what operation needs to be performed to find the
unknown number.
SolutionFirst, we translate.
is of
x  160%  15.8 xis the amount, 160% is the percent,
and 15.8 is the base.
Now we solve the equation by performing the multiplication on the right side.
Write 160% as a decimal: 160% 1.6.
Do the multiplication.
Thus, 25.28 is 160% of 15.8. In this case, the amount exceeds the base because the
percent is more than 100%.
x25.28
15.8
1.6
948
1580
25.28
x1.615.8
What number 160% 15.8?
Self Check 3
What number is 240% of 80.3?
Now TryProblem 23
    
3 Solve percent equations to find the percent.
In the drinking water problem (Type 2 from the newspaper), we must find the percent.
Once again, we translate the words of the problem into a percent equation and solve it.