Basic Mathematics for College Students

528 Chapter 6 Percent

Self Check 10

PRESIDENTIAL ELECTIONSResults

from the 2004 U.S. presidential

election are shown in the circle

graph below. Find the number

of states won by President Bush.

John

Kerry

38%

President

Bush

62%

2004 Presidential Election

States won by each candidate

Now TryProblem 85







 

    

50

 0.56

300

25 00

28.00

EXAMPLE (^10) Presidential Elections
Results from the 2008 U.S. presidential election are
shown in the circle graph to the right. Find the
number of states won by Barack Obama.
StrategyWe will rewrite the facts of the problem
in percent sentence form.
WHYThen we can translate the sentence to a
percent equation (or percent proportion) to find the number of states won by
Barack Obama.
SolutionThe circle graph shows that Barack Obama won 56% of the 50 states.
Thus, the percent is 56% and the base is 50. One way to find the unknown amount
is to write and then solve a percent equation.
is of
x  56%  50 Translate to a percent equation.
Now we perform the multiplication on the right side of the equation.
Write 56% as a decimal: 56% 0.56.
Do the multiplication.
Thus, Barack Obama won 28 of the 50 states in the 2008 U.S. presidential election.
Another way to find the unknown amount is to write and then solve a percent
proportion.
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 right side, do the multiplication:
50  14 700.
To undo the multiplication by 25 and isolate x
on the left side, divide both sides of the equation
by 25. Then remove the common factor of 25 from
the numerator and denominator.
On the right side, divide 700 by 25.
As we would expect, the percent proportion method gives the same answer as the
percent equation method. Barack Obama won 28 of the 50 states in the 2008 U.S.
presidential election.
x 28
x 25
1
25
1



700

25

x 25  700

x

50 

14

x 25  50  14 25

56

100



4

1

 14

4

1

 25



14

25

x

50



14

25

10056

x

50



56

100

amount percent base

What number 56% 50?

x 28

x0.56 50

What number 56% 50?

John

McCain

44%

Barack

Obama

56%

2008 Presidential Election

States won by each candidate

28

25  700

 50

200

 200

0

50

 14

200

500

700