Page 53 - Algebra 1

Example
2
Converting Units of Area
A gym measures 8.5 meters by 14 meters. The owner bought mats to cover the floor. Each mat is 110 centimeters square. If 95 mats were purchased, are there enough mats to cover the floor?
SOLUTION Find the area and convert the unit of measure.
Math Reasoning
Each mat is 110
centimeters square.
This means that the length and width are 110 centimeters each.
8.5 m · 14 m = 119 m2 119 m2 ? cm2
1_m = 1 0 0 c m
Find the area of the room. Write the conversion. Equate units.
Write a unit ratio.
Write the multiplication sentence.
Cancel out common factors.
Multiply.
Find the area of 95 mats. Compare the areas.
100 cm 1m
119m·m· 100cm · 100cm __
1m 1m
=119m·m· 100cm · 100cm __
1m 1m
= 119·100cm·100cm =1,190,000cm
__ 1
95(110 cm · 110 cm) = 1,149,500 cm2 1,149,500 cm2 < 1,190,000 cm2
2
The area covered by 95 mats is less than the area of the floor, so there are not enough mats to cover the floor.
Application: Converting Units of Volume
A hose with a flow rate of 41,472 cubic inches per hour is filling up a pool. The volume of the pool is 1,104 cubic feet. How many hours will it take to fill the pool?
SOLUTION Find the volume and convert the unit of measure.
Example
3
Math Reasoning
Analyze Compare the process of converting feet to inches with the process of converting feet per minute to inches per minute.
41,472 in ? ft3 _3_
Identify known and missing information.
Equate units. Write a unit ratio.
Write the multiplication sentence.
Cancel out common factors.
Multiply.
1 hour
1_ f t = 1 2 i n . 1 ft
1 hour
41,472in.·in.·in. · 1ft · 1ft · 1ft _____
1hr 12in. 12in. 12in.
12 in.
= 41,472in.·in.·in. · 1ft · 1ft · 1ft _____
24
1hr
12in. 12in. 12in. 111
38 Saxon Algebra 1
24 ft ___3
= 24ft·ft·ft =
1 hr 1 hr
1,104 ÷ 24 = 46 hours
It will take 46 hours to fill the pool.