Ratios and Proportions - Basic Mathematics for Water and Wastewater Operators - page 130

3. Cross-multiplying solves ratio problems; that is, we multiply the left numer-
ator ( A ) by the right denominator ( D ) and say that the product is equal to the
left denominator ( B ) times the right numerator ( C ):

A × D = B × C

AD = BC

4. If one of the four items is unknown, we can solve the ratio by dividing the
two known items that are multiplied together by the known item that is
multiplied by the unknown. For example, if 2 pounds of alum are needed to
treat 500 gallons of water, how many pounds of alum are required to treat
10,000 gallons? We can state this as a ratio: 2 pounds of alum is to 500 gal-
lons of water as x pounds of alum is to 10,000 gallons. This is set up in this
manner:

1lbalum
500 galwater

lb alum
10,000 gal

x

=

water

Cross-multiplying:

500 ×=× x 110 000 ,

Transposing:

110 000
500

× ,

x = = 20 lb alum

For calculating a proportion, suppose that 5 gallons of fuel cost $5.40. How
much would 15 gallons cost?

5gal
$5.40

15 gal

=

x

5 ×= × x 5 40 15

54015
5

.
. ×

x =

81

x =

5
16 20 x = $.

■ Example 9.1
Problem: If a pump will fill a tank in 20 hours at 4 gallons per minute (gpm), how
long will it take a 10-gpm pump to fill the same tank?