7th - Chapter 6 Review 25

Ratios

100

Write 60 girls to 80 boys as a ratio in 3 ways.

3/4, 3 to 4, 3:4

200

Write 18 limes to 30 lemons as a ratio in 3 ways.

3:5, 3/5, 3 to 5

300

In a locked box, there are jolly ranchers and life savers. The amount of life savers in the box is five more than one-third of the amount of jolly ranchers. If there are 45 jolly ranchers in the box, what is the ratio of jolly ranchers to life savers expressed as a fraction?

1/3(45)+5 = 15+5 = 20

45/20 =  9/4 

400

In a vending machine there are 8 bags of chips. The number of candy bars in the machine are six less than twice the amount of chips, and there are twice as many bottles of water than candy bars. What is the ratio of bags of chips to water bottles?

Candy bars: 2(8) - 6 = 16 - 6 = 10

Water bottles: 2(10) = 20

chips to water bottles: 8:20 = 2:5

500

A baseball team has pitchers and position players. The amount of pitchers is three less than the amount of position players. If there are 27 players currently on the team, what is the ratio of pitchers to position players?

Position players: x

Pitchers: x-3

x + x-3 = 27

2x-3 = 27

2x = 30

x = 15                15 position players, 12 pitchers

12/15 = 4/5

Ratios with Conversions

100

What is the ratio of 2 gallons to 7 quarts

4 quarts per gallon

8:7

200

What is the ratio of 40 inches to 3 feet?

1 ft = 12 inches

40:3x12

40:36

10:9

300

What is the ratio of 88 ounces to 5 pounds?

1 pound = 16 oz

88:5(16)

88:80

11:10

400

What is the ratio of 7 minutes to 140 seconds?

1 minute = 60 seconds

7x60:140

420:140

3:1

500

What is the ratio of 2 gallons to 24 cups?

1 gallon = 4 quarts 

1 quart = 2 pints

1 pint = 2 cups

2 gallons x 4 x 2 x 2 = 32

32:24 = 4:3

Unit Rate

100

If Mimi drives 350 miles in 5 hours, what is her rate of speed (miles per hour)?

What is 70 miles per hour

200

If James types 120 words per 3 minutes, how many words can he type in 10 minutes?

120/3 = 40

40 x 10 = 400 words

300

If 10 bags of Hot Cheetos cost $3.50, then about how many bags can you buy with $10?

$0.35/bag

.35/1 = 10/x

.35x = 10

x = 28 bags

400

Which is the better deal $120 for 15 t-shirts or $30 for 4 t-shirts

120/15 = $8/shirt

30/4 = $7.50/shirt

30/4 is the better buy

500

Tracy is running 6.8 meters per second. At this rate, how long will it take for her to complete her 100m dash? Round your answer to the nearest hundredth.

Use a proportion:

6.8/1 = 100/x

6.8x = 100

x = 14.71 s

Solving Proportions

100

Solve for x. x/6 = 6/9

What is 4

200

Solve for x.   (3x)/2 = 9/6 

(3x)/2 = 9/6

3x xx 6 = 9 xx 2

18x = 18

x = 1

300

Solve for x. 

(x+1)/6 = 8/12

(x+1)/6 = 8/12

12(x+1) = 6 xx 8

12x+12 = 48

12x = 36

x = 3

400

Solve for x.  3/(x-4) = 2/(x+3) 

3/(x-4) = 2/(x+3)

3(x+3) = 2(x-4)

3x+9 = 2x-8

x = -17

500

Solve for x. 

3/(10-2x)= 9/(5x+19)

3/(10-2x)= 9/(5x+19)

3(5x+19) = 9(10-2x)

15x + 57 = 90 - 18x

33x = 33

x = 1

Word Problems

100

A 54 inch long ribbon is cut into 3 strips in the ratio of 2:3:4. What is the length of the longest piece?

2+3+4 = 9 parts

54/9 means each part is 6 inches

The longest piece is 4x6 or 24 inches

200

The ratio of red to blue to purple jolly ranchers in one bag is 4:3:8. If there are 80 purple jolly ranchers, how many jolly ranchers are there altogether?

80/8 = 10 jolly ranchers per part

4x10 = 40 red

3x10 = 30 blue

8x10 = 80 purple

40+30+80 = 150 jolly ranchers

300

A store sells basketball jerseys for a local team. The ratio of gray to blue jerseys is 5:2. The ratio of the number of blue to white is 3:5. What is the ratio of gray to white jerseys?

Blue jerseys is listed in both ratios, so find LCM.

LCM of 2 and 3 is 6. Make equivalent ratios so the parts of blue jerseys are the same

5:2 becomes 15:6 and 3:5 becomes 6:10

So the ratio of gray to white is 15:10, which is 3:2

400

Ms. Lopez had some drinking glasses. The ratio of the number of blue glasses to the number of white glasses was 5 : 6. Her children broke 8 blue glasses and the ratio became 13 : 18. Part A How many white glasses did she have?

# of White glasses stays the same, so find LCM between 6 and 18 and make equivalent ratios

So 5:6 becomes 15:18, which means the parts of blue glasses decreased from 15 to 13 (2 parts). Since they broke 8 blue glasses (2 parts) then each part is 4 glasses. If she has 18 parts white glasses, then 18x4 = 72 white glasses

500

David and Sarah are siblings. They have saved their allowances in the ratio of 9:7. Sarah wants to use her savings to buy something, but she had to borrow $15 dollars from David. After David lent her the money and before she made the purchase, the ratio of the siblings' savings was 13:19. How much money did Sarah have to make the purchase?

Overall $$ does not change, so 9+7 = 16 parts

and 13+19 = 32 parts. They represent the same amount of money, so find LCM of 16 and 32 and make equivalent ratios.

9:7 becomes 18:14.  David's #of parts decreased by 5 and Sarah's number of parts increased by 5, which means the $15 is divided by 5 and 1 part = $3. Sarah has 19 parts altogether, so she has 3x19 = $57