Basic Math Operations - Mathematics and Statistics for the Environment - page 51

to treat 10,000 gal? We can state this as a ratio: “2 lb of alum is to 500 gal of water as x lb
of alum is to 10,000 gal of water.” This is set up in this manner:

1lbalum
500 galwater

lb alum
10,000 gal

x

=

water

Cross-multiplying,

500 × x = 1 × 10,000

Transposing,

110 000
500

× ,

= 20 lb alum

To calculate proportion, suppose, for example, that 5 gal of fuel costs $5.40. What will 15
gal cost?

5gal
$5.40

15 gal

=

$ y

5 gal ×= × y 15 gal $. 5 40 = 81

81
5

y === $. 16 20

■ EXAMPLE 2.27
Problem: If a pump will fill a tank in 20 hr at 4 gpm, how long will it take a 10-gpm pump to fill
the same tank?

Solution: First, analyze the problem. Here, the unknown is some number of hours. But, should the
answer be larger or smaller than 20 hr? If a 4-gpm pump can fill the tank in 20 hr, a larger (10-gpm)
pump should be able to complete the filling in less than 20 hr. Therefore, the answer should be less
than 20 hours. Now set up the proportion:

hr
20 hr

x 4 gpm

10 gpm

=

( 420 × )

x = = 8hr

10

■ EXAMPLE 2.28
Problem: Solve for the unknown value x in the problem given below.

Solution:

36
180

x

=

4450

4450 × 36

== x 890

180