Page 476 - Basic College Mathematics with Early Integers

S E C T I O N 6.2 I SOLVING PERCENT PROBLEMS USING EQUATIONS 453

After a percent problem has been written as a percent equation, we can use the
equation to find the unknown number.This is called solving the equation.

Example 7 Solving Percent Equation for the Amount PRACTICE 7
What number is 20% of 85?
What number is 35% of 40?
T T T T T
Solution: n = 35% # 40 Translate to an equation.
n = 0.35 # 40 Write 35% as 0.35.
n = 14 Multiply 0.35 40 = 14.
#
Thus, 14 is 35% of 40.
Is this reasonable? To see, round 35% to 40%.Then 40% of 40 or 0.40(40) is 16.
Our result is reasonable since 16 is close to 14.
Work Practice 7

When solving a percent equation, write the percent as a decimal (or fraction).

Example 8 Solving Percent Equation for the Amount PRACTICE 8
90% of 150 is what number?
85% of 300 is what number?
5
T T T T T
Solution: 85% # 300 = n Translate to an equation.
0.85 # 300 = n Write 85% as 0.85.
#
255 = n Multiply 0.85 300 = 255.
Thus, 85% of 300 is 255.
Is this result reasonable? To see, round 85% to 90%.Then 90% of 300 or
0.90(300) = 270, which is close to 255.
Work Practice 8

Example 9 Solving Percent Equation for the Base PRACTICE 9
15% of what number is 1.2?
12% of what number is 0.6?
5
T T T T T
Solution: 12% # n = 0.6 Translate to an equation.
0.12 # n = 0.6 Write 12% as 0.12.
Recall from Section 5.3 that if “0.12 times some number is 0.6,” then the number
is 0.6 divided by 0.12.
0.6
n = Divide 0.6 by 0.12, the number multiplied by n.
0.12
n = 5
Thus, 12% of 5 is 0.6.
Is this reasonable? To see, round 12% to 10%.Then 10% of 5 or 0.10(5) = 0.5 ,
which is close to 0.6.
Answers
Work Practice 9 7. 17 8. 135 9. 8