Page 206 - Algebra 1

b. An engineer opens a valve that drains 60 gallons of water per minute from a tank. How many quarts were drained per second?
Use a conversion factor to change gallons to quarts. Then simplify.
Use a conversion factor to change minutes to seconds. Then simplify.
SOLUTION
60 gallons = ? quarts __
Caution
Set up the conversion factor so the units of measure cancel.
1 gallon 4 quarts
Use the factor
4 quarts , not 1 gallon . __
1 minute 1 second
60 gallons · 4 quarts = 240 quarts ___
1 gallon
1 minute _
A proportion is an equation that shows two ratios are equal. The equation _3 = _9 is a proportion.
Solving Proportions Using Cross Products
1 minute
240 quarts · _
1 minute
= 240 quarts _ 4 _
60 seconds
The tank drains at a rate of 4 quarts per second.
1 minute
60 1 seconds
5 15
Solve each proportion. a. _x =_2
15 3
SOLUTION
_x = _2 15 3
3 · x = 15 · 2 3x = 30
b.
Write the cross products. Simplify.
Solve.
Write the cross products. Distribute and multiply. Simplify.
Solve.
Cross Products Property
If _a = _c and b ≠ 0 and d ≠ 0, then ad = bc. bd
In _a = _c , ad and bc are the cross products. bd
Example
3
x = 10 x-1=1
__ 12 6
SOLUTION
x-1=1 __
12 6 6(x - 1) = 12(1)
6x - 6 = 12 6x = 18
x = 3
Lesson 31 191