Page 159 - ArithBook5thEd ~ BCC

9. 250 is what percent of 325? (Round to the nearest tenth of a percent.)

10. 108 is 80% of what number?

11. A baseball team won 93 games, or 62% of the games it played. How many games did the team
play?

12. New York State sales tax is 8.25%. If the sales tax on a DVD player is $16.50, what is the
(before-tax) price of the player?

13. Marina’s annual salary last year was $56, 000. This year she received a raise of $4, 480. By what
percent did her salary increase?

14. A town’s population decreased from 13, 000 to 12, 220. By what percent did the population de-
crease?

5.4 Rates

There are lots of real-world quantities which compare in a fixed ratio. For example, for any given car,
the ratio of miles driven to gallons of gas used,
miles
or “miles per gallon”
gallon

is essentially unchanging, or fixed. If we know, say, that 5 gallons of gas was needed to drive 150
miles, we can predict the amount that will be needed to drive any other distance, by solving a simple
proportion.
Example 200. Maya used 5 gallons of gas to drive 150 miles. How many gallons will she need to drive
225 miles?

Solution. We solve the proportion
150 miles 225 miles
= ,
5gallon x gallons
where x represents the number of gallons she will need. Before setting the cross-products equal, reduce
30
the fraction on the left side to .Then
1
30x =225 (5.2)
225 1
x = =7 .
30 2
1
She will need 7 gallons of gas to drive 225 miles.
2
Miles per gallon is an example of a rate, or comparison of unlike quantities by means of a ratio. In
the example above, the miles per gallon rate for Maya’s car was
150 miles 150 30
= = or 30 miles per gallon.
5gallons 5 1

Other examples of rates are: dollars per hour (pay rate for an hourly worker), dollars per item (price of
an item for sale), calories per minute (energy use by an athlete). You can undoubtedly think of many
others.

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