Basic Mathematics for College Students

To solve percent application problems, we often have to rewrite the facts of the
problem in percent sentence form before we can translate to an equation.

6.2 Solving Percent Problems Using Percent Equations and Proportions 519

Success Tip Sometimes the calculations to solve a percent problem are made

easier if we write the percent as a fraction instead of a decimal. This is the case

with percents that have repeatingdecimal equivalents such as 33 31 %, 66 32 %, and

. You may want to review the table of percents and their fractional
equivalents on page 508.

16 23 %

EXAMPLE (^8) 31.5 is of what number?
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 we can solve the equation to find the unknown number.
SolutionFirst, we translate.
is of
31.5 x 31.5 is the amount, is the percent,
and xis the base.
In this case, the calculations can be made easier by writing as a fraction
instead of as a repeating decimal.
Recall from Section 6.1 that.
To undo the multiplication by and isolate xon the right side of
the equation, divide both sides by.
To simplify the fraction on the right side of the equation, remove
the common factor of from the numerator and denominator.
On the left side, the fraction bar indicates division.
On the left side, write 31.5 as a fraction:.
Then use the rule for dividing fractions:
Multiply by the reciprocal of , which is.
Do the multiplication.
Thus, 31.5 is 33 13 %of 94.5.
94.5x
31 31
31.5 1
31.5
1



3

1

x

31.5

1

3

x

(^13)

31.5

1

3



1

3

1

x

1

3

1

31

31

31.5

1

3



1

3

x

1

3

31.5 33 31 % 31

1

3

x

33 13 %

33 13 % 33 31 %

31.5 33 13 % what number?

33 13 %

Self Check 8

150 is of what number?

Now TryProblems 43 and 83

66 23 %

31

1

.5

 3

94.5

EXAMPLE (^9) Rentals In an apartment complex, 198 of the units are
currently occupied. If this represents an 88% occupancy rate, how many units are
in the complex?
StrategyWe will carefully read the problem and use the given facts to write them
in the form of a percent sentence.
Self Check 9
CAPACITY OF A GYMA total of 784
people attended a graduation in a
high school gymnasium. If this was
98% of capacity, what is the total
capacity of the gym?