Basic Mathematics for College Students

6.3 Applications of Percent 541

Self Check 6

HOME SCHOOLINGIn one school

district, the number of home-

schooled children increased from

15 to 150 in 4 years. Find the

percent of increase.

Now TryProblem 33

 







EXAMPLE (^6) JFK A 1996 auction included
an oak rocking chair used by President John F.
Kennedy in the Oval Office. The chair, originally
valued at $5,000, sold for $453,500. Find the percent
of increase in the value of the rocking chair.
StrategyWe will begin by finding the amount of
increase in the value of the rocking chair.
WHYThen we can calculate what percent of the
original $5,000 value of the chair that the increase
represents.
SolutionFirst, we find the amount of increase in
the value of the rocking chair.
Subtract the original value from
the price paid at auction.
The rocking chair increased in value by $448,500. Next, we find what percent of the
original $5,000 value of the rocking chair the $448,500 increase represents by
translating the problem into a percent equation (or percent proportion) and solving it.
The percent equation method:
is of
448,500  x  5,000 Translate.
This is the equation to solve.
To isolate xon the right side, divide both sides of the equation
by 5,000. Then remove the common factor of 5,000 from the
numerator and denominator.
Before performing the division on the left side of the equation,
recall that there is a shortcut for dividing a dividend by a divisor
when both end with zeros. Remove two of the ending zeros in the
divisor 5,000 and remove the same number of ending zeros in the
dividend 448,500.
Divide 4,485 by 50.
To write the decimal 89.7 as a percent, multiply it by
100 by moving the decimal point two places to the right,
and then insert a % symbol.
The percent proportion method:
is of
This is the proportion to solve.
To solve the proportion, find the cross products. Then
set them equal.
To simplify the left side of the equation, do the
multiplication: 448,500  100 44,850,000.
44,850,0005,000x
448,500 100 5,000x

448,500

5,000



x

100

amount percent base

$448,500 what percent $5,000?

8,970%x

8970%x

89.7x

4,485

50

x

448,500

5,000



x5,000

1

5,000

1

448,500x5,000

$448,500 what percent $5,000?

453,5005,000448,500

89.7

50  4,485.0

 400

485

 450

35 0

 35 0

0

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