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DSPM Chapter 8 Review: Solving Proportions and Variations, Study notes of Algebra

Southwest Tennessee Community CollegeAlgebra

Solutions to various proportions and direct/inverse variation problems. Students can use this review as a study aid to understand the concept of proportions and how to apply it to solve real-life problems. Calculations and answers for 15 problems, covering topics such as cross-multiplication, direct variation, and inverse variation.

Typology: Study notes

Pre 2010

Uploaded on 08/18/2009

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Name___________________
DSPM 0800 CHAPTER 8 REVIEW
Instructions: Show all calculations.
Solve the following proportions. Round solutions to the nearest thousandth:
Proportions are solved by using cross-multiplication:
If
a c
b d
, then ad = bc.
1.
7
9 10
a
7
9 10
10 9(7)
10 63
6.3
a
a
a
a
2.
7 5
2 8
x
46
8
23
4
7 5
2 8
8(7 ) 2(5)
56 8 10
56 8 56 10 56
8 46
5.75
x
x
x
x
x
x
x
x




pf3
pf4
pf5

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Download DSPM Chapter 8 Review: Solving Proportions and Variations and more Study notes Algebra in PDF only on Docsity!

Name___________________ DSPM 0800 CHAPTER 8 REVIEW Instructions: Show all calculations. Solve the following proportions. Round solutions to the nearest thousandth: Proportions are solved by using cross-multiplication: If a c b d  , then ad = bc.

a 7 9 10 10 9(7) 10 63

a a a a

x 46 8 23 4

x x x x x x x x              

x x 2 1 7 3 9 9(2 1) 7( 3) 18 9 7 21 18 9 7 7 21 7 11 9 21 11 9 9 21 9 11 30 x x x x x x x x x x x x x

30 11

x x

r

r r r r r

x  4 4 3 4 19 4(19) 4(3 4) 76 12 16 76 16 12 16 16 60 12 5 x x x x x x

  1. If 6 cans of coffee cost $18.75, how much do 14 cans cost? 6 cans $18. 14 cans 6 14(18.75) 6 262.

x x x x

6 cans of coffee cost $43.75.

  1. A map has a scale of 2 in. = 135 mi. How far is the distance which measures 5 12 in. on the map? 1 2 11 2 2 in. 135 mi. 5 in. mi. 2 (135) (or use 5.5 in.) 2 742.

x x x x

The distance is 371.25 miles.

  1. There are 10 women in a class of 25 students. If the students in the college are in this same proportion, how many women are enrolled if the total enrollment is 15,900? 10 women 25 students women 15,900 students 10(15,900) 25 159, 000 25 6, x x x x

There are 6,360 women enrolled in the college.

  1. A 20-oz. bottle of soda costs $1.57 and a 32-oz. bottle of soda costs $2.46. Compute the unit price for each bottle. Then identify the better buy. The unit cost is the cost per ounce. The better buy is the item with the lowest cost per ounce. $1. $0.0785 / oz. 20 oz. $2. $0.076875 / oz. 32 oz.

The 32-oz. bottle is the better buy.

  1. A gear measures 8 in. across. It turns at 800 rpm. If it is connected to another gear that turns at 250 rpm, what is the diameter of the other gear? The larger gear will be the slower gear. 8 in. 250 rpm in. 800 rpm 8(800) 250 6, 400 250
  2. x x x x

The other gear measures 25.6 in.

  1. If it takes 60 oz. of grass seed to seed 3, 000 ft 2 of lawn, how much grass seed will it take to seed 5, 000 ft 2 of lawn? 2 2 60 oz. 3, 000 ft oz. 5, 000 ft 60(5, 000) 3, 000 300, 000 3, 000 100 x x x x

It will take 100 oz. of grass seed.

  1. The volume of a gas is inversely proportional to the pressure on it. If a gas has a volume of (^) 375 in 3 , under a pressure of 32 pounds per square inch (psi), what will the volume be if the pressure is decreased to 24 psi? Round to the nearest tenth of a cubic inch. 3 3 375 in 24 psi in 32 psi 375(32) 24 12, 000 24 500 x x x x

The volume is (^) 500 in 3.