Basic Mathematics for College Students

6.2 Solving Percent Problems Using Percent Equations and Proportions 527

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?

Now TryProblem 81







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.
WHYThen we can write and solve a percent proportion to find the unknown
number of units in the complex.
SolutionAn occupancy rate of 88% means that 88% of the units are occupied.
Thus, the 198 units that are currently occupied are 88% of some unknown number
of units in the complex, and we can write:
is of
This is the proportion to solve.
To make the calculations easier, it is helpful to simplify the ratio at this time.
On the right side, simplify:.
Find the cross products. Then set them equal.
To simplify the left side, do the multiplication:
198  25 4,950.
To undo the multiplication by 22 and isolate x
on the right side, divide both sides of the equation
by 22. Then remove the common factor of 22 from
the numerator and denominator.
On the left side, divide 4,950 by 22.
The apartment complex has 225 units, of which 198, or 88%, are occupied.
225 x

4,950

22



x 22

1

22

1

4,950x 22

198  25 x 22

88

100



4

1

 22

4

1

 25



22

25

198

x



22

25

10088

198

x



88

100

amount percent base

198 88% what number?

198

 25

990

3960

4,950

5 Read circle graphs.

Percents are used with circle graphs,or pie charts,as a way of presenting data for
comparison. In the figure below, the entire circle represents the total amount of
electricity generated in the United States in 2008. The pie-shaped pieces of the graph
show the relative sizes of the energy sources
used to generate the electricity. For example,
we see that the greatest amount of electricity
(50%) was generated from coal. Note that if
we add the percents from all categories
(50% 3% 7% 18% 20% 2%), the
sum is 100%.
The 100 tick marks equally spaced
around the circle serve as a visual aid when
constructing a circle graph. For example, to
represent hydropower as 7%, a line was
drawn from the center of the circle to a tick
mark. Then we counted off 7 ticks and drew
a second line from the center to that tick to
complete the pie-shaped wedge.

Other

2%

Sources of Electricity in

the United States, 2008

Coal

50%

Nuclear

20%

Natural

gas

18%

Hydropower

7% Petroleum3%

Source: Energy Information Administration

225

22  4,950

 44

55

 44

110

 110

0