Basic Mathematics for College Students

518 Chapter 6 Percent

SolutionFirst, we translate.

of is

x  6  7.5

This is the equation to solve.

To undo the multiplication by 6 and isolate xon the left

side of the equation, divide both sides by 6.

To simplify the fraction on the left side of the equation,

remove the common factor of 6 from the numerator and

denominator. On the right side, divide 7.5 by 6.

To write the decimal 1.25 as a percent, multiply it

by 100 by moving the decimal point two places to

the right, and then insert a % symbol.

Thus, 7.5 is 125% of 6.

x125%

x1 25%

x1.25

x 6

1

6

1

1.25

x 6

6



7.5

6

x 6 7.5

What percent 6 7.5

1.25

(^6)  7.50
 6
1 5
 1 2
30
 30
0
    
 

4 Solve percent equations to find the base.
In the percent problem about the State Board of Examiners (Type 3 from the
newspaper), we must find the base. As before, we translate the percent sentence into
a percent equation and then find the unknown number.
EXAMPLE (^7) 6 is 75% 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
6  75%  x 6 is the amount, 75% is the percent,
and xis the base.
Now we solve the equation.
Write 75% as a decimal: 75% 0.75.
To undo the multiplication by 0.75 and isolate xon the
right side, divide both sides of the equation by 0.75.
To simplify the fraction on the right side of the equation,
remove the common factor of 0.75. On the left side,
divide 6 by 0.75.
Thus, 6 is 75% of 8. That is, there are 8 members on the State Board of Examiners
mentioned in the newspaper article.
8 x

8 

0.75x

1

0.75

1

6

0.75



0.75x

0.75

6 0.75x

6 75% what number?

Self Check 7

3 is 5% of what number?

Now TryProblem 39

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

8

(^75)  600
 600
0