Basic Mathematics for College Students

516 Chapter 6 Percent

The Language of Mathematics We solve percent equations by writing

a series of steps that result in an equation of the form xa numberor

a numberx.We say that the variable xis isolatedon one side of the

equation.Isolatedmeans alone or by itself.

EXAMPLE (^4) 38 is what percent of 40?
StrategyWe will look for the key words is, of,and what
percentin the percent sentence and translate them to
mathematical symbols to form a percent equation.
WHYThen we can solve the equation to find the unknown
percent.
SolutionFirst, we translate.
is of
38  x  40 38 is the amount, xis the percent, and
40 is the base.
This is the equation to solve.
On the right side of the equation, the unknown number xis multiplied by 40. To
undo the multiplication by 40 and isolate x,we divide both sides by 40.
We can simplify the fraction on the right side of the equation by removing the
common factor of 40 from the numerator and denominator. On the left side, we
perform the division indicated by the fraction bar.
To simplify the left side, divide 38 by 40.
Since we want to find the percent, we need to write the decimal 0.95 as a percent.
To write 0.95 as a percent, multiply it by 100 by moving the decimal point
two places to the right, and then insert a % symbol.
We have found that 38 is 95% of 40. That is, 95% of the wells mentioned in the
newspaper article were declared safe.
95%x
0 95%x
0.95x

0.95

x 40

1

40

1

38

40



x 40

40

38 x 40

38 what percent 40?

Self Check 4

4 is what percent of 80?

Now TryProblems 27 and 79

Circulation Monday, March 23 50 cents

Transit Strike Averted!

Drinking Water38 of 40 Wells

Declared Safe

500-member unionLabor: 84% of

votes to acceptnew offer

New Appointees

These six area residentsnow make up 75% of the

State Board of Examiners

    

    

0.95

(^40)  38.00
 36 0
200
 200
0

EXAMPLE (^5) 14 is what percent of 32?
StrategyWe will look for the key words is, of,and what percentin the percent
sentence and translate them to mathematical symbols to form a percent equation.
WHYThen we can solve the equation to find the unknown percent.
SolutionFirst, we translate.
is of
14  x  32 14 is the amount, xis the percent, and
32 is the base.
14 what percent 32?
Self Check 5
9 is what percent of 16?
Now TryProblem 31
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