514 Chapter 6 Percent
EXAMPLE (^1) Translate each percent sentence to a percent equation.
a.What number is 12% of 64?
b.What percent of 88 is 11?
c.165% of what number is 366?
StrategyWe will look for the key words is, of,and what number (or what percent)
in each percent sentence.
WHYThese key words translate to mathematical symbols that form the percent
equation.
SolutionIn each case, we will let the variable represent the unknown number.
However, any letter can be used.
a. is of This is the given percent sentence.
x 12% 64 This is the percent equation.
b. of is This is the given percent sentence.
x 88 11 This is the percent equation.
c. of is This is the given percent sentence.
165% x 366 This is the percent equation.
165% what number 366?
What percent 88 11?
What number 12% 64?
x
Self Check 1
Translate each percent sentence
to a percent equation.
a.What number is 33% of 80?
b.What percent of 55 is 6?
c.172% of what number is 4?
Now TryProblem 17
2 Solve percent equations to find the amount.
To solve the labor union percent problem (Type 1 from the newspaper), we translate
the percent sentence into a percent equation and then find the unknown number.
EXAMPLE (^2) What number is 84% of 500?
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 it will be clear what operation should be
performed to find the unknown number.
SolutionFirst, we translate.
is of
x 84% 500 Translate to a percent equation.
Now we perform the multiplication on the right side of the equation.
Write 84% as a decimal: 84% 0.84.
Do the multiplication.
We have found that 420 is 84% of 500. That is, 420 union members mentioned in the
newspaper article voted to accept the new offer.
x 420
x0.84 500
What number 84% 500?
Self Check 2
What number is 36% of 400?
Now TryProblems 19 and 71 CirculationTransit Strike Averted!Monday, March 23 50 cents
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
The Language of Mathematics When we find the value of the variable that
makes a percent equation true, we say that we have solved the equation.In
Example 2, we solvedx84% 500 to find that the variable xis 420.
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