The unit rate is 3.5 meters per second.
1-1 Rates
Find the unit rate. Round to the nearest
hundredth if necessary.
1. 360 miles in 6 hours
ANSWER: 3.5 m/s
4. $7.40 for 5 pounds
SOLUTION: SOLUTION: The unit rate is $1.48 per pound.
The unit rate is 60 miles per hour.
ANSWER: 60 mi/h
2. 6,840 customers in 45 days
SOLUTION: The unit rate is 152 customers per day.
ANSWER: 152 customers per day
3. 45.5 meters in 13 seconds
SOLUTION: ANSWER: $1.48/lb
5. Estimate the unit rate if 12 pairs of socks sell for
$5.79.
SOLUTION: Sample solution: Round $5.79 up to $6.00.
The unit rate is about $0.50 per pair of socks.
ANSWER: Sample answer: about $0.50 per pair
6. Justify Conclusions The results of a swim meet
are shown. Who swam the fastest? Explain your
reasoning.
The unit rate is 3.5 meters per second.
ANSWER: 3.5 m/s
4. $7.40 for 5 pounds
SOLUTION: eSolutions Manual - Powered by Cognero
The unit rate is $1.48 per pound.
SOLUTION: Find the unit rate for each swimmer.
Tawni
50 meters ÷ 40.8 seconds ≈ 1.2255 m/s
Pepita
100 meters ÷ 60.2 seconds ≈ 1.6611 m/s
Susana
200 meters ÷ 112.4 seconds ≈ 1.7794 m/s
1.78 m/s > 1.66 m/s > 1.23 m/s
Susana’s rate is the fastest because she travels the
farthest in one second.
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ANSWER: Susana; Sample answer: 1.78 m/s > 1.66 m/s > 1.23
The unit rate is about $0.50 per pair of socks.
ANSWER: 1-1 Rates
Sample answer: about $0.50 per pair
6. Justify Conclusions The results of a swim meet
are shown. Who swam the fastest? Explain your
reasoning.
Since Ben can type 51 words in 1 minute, he can
type 51 × 10 or 510 words in 10 minutes.
ANSWER: 510 words
8. Kenji buys 3 yards of fabric for $7.47. Later he
realizes that he needs 2 more yards. How much will
he pay for the extra fabric?
SOLUTION: Find the unit rate. Then multiply by 2 to find the cost
for 2 yards of fabric.
SOLUTION: Find the unit rate for each swimmer.
Tawni
50 meters ÷ 40.8 seconds ≈ 1.2255 m/s
Pepita
100 meters ÷ 60.2 seconds ≈ 1.6611 m/s
Susana
200 meters ÷ 112.4 seconds ≈ 1.7794 m/s
1.78 m/s > 1.66 m/s > 1.23 m/s
Susana’s rate is the fastest because she travels the
farthest in one second.
ANSWER: Susana; Sample answer: 1.78 m/s > 1.66 m/s > 1.23
m/s
7. Ben can type 153 words in 3 minutes. At this rate,
how many words can he type in 10 minutes?
SOLUTION: Find the unit rate. Then multiply this unit rate by 10 to
find the number of words he can type in 10 minutes.
Since Kenji pays $2.49 per yard for the first 3 yards
of fabric, he will pay $2.49 × 2 or $4.98 for the extra 2 yards of fabric.
ANSWER: $4.98
9. The record for the Boston Marathon's wheelchair
division is 1 hour, 18 minutes, and 27 seconds.
a. The Boston Marathon is 26.2 miles long. What
was the average speed of the record winner of the
wheelchair division? Round to the nearest hundredth.
b. At this rate, about how long would it take this
competitor to complete a 30-mile race?
SOLUTION: a. Think of 1 hour, 18 minutes and 27 seconds as a
sum of 1 +
+ .
Since Ben can type 51 words in 1 minute, he can
type 51 × 10 or 510 words in 10 minutes.
ANSWER: 510 words
8. Kenji buys 3 yards of fabric for $7.47. Later he
realizes that he needs 2 more yards. How much will
he pay for the extra fabric?
SOLUTION: Find the unit rate. Then multiply by 2 to find the cost
for 2 yards of fabric.
The average speed of the record winner of the
wheelchair division is about 20.04 miles per hour.
b. Divide the distance by the average speed to find
the time.
≈ 1.4970 hours
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So, it would take this competitor about 1.5 hours to
complete a 30-mile race.
of fabric, he will pay $2.49 × 2 or $4.98 for the extra 2 yards of fabric.
ANSWER: 1-1 Rates
$4.98
9. The record for the Boston Marathon's wheelchair
division is 1 hour, 18 minutes, and 27 seconds.
a. The Boston Marathon is 26.2 miles long. What
was the average speed of the record winner of the
wheelchair division? Round to the nearest hundredth.
b. At this rate, about how long would it take this
competitor to complete a 30-mile race?
complete a 30-mile race.
ANSWER: a. 20.04 mi/h
b. about 1.5 h
10. At Tire Depot, a pair of new tires sells for $216. The
manager’s special advertises the same tires selling at
a rate of $380 for 4 tires. How much do you save per
tire if you purchase the manager’s special?
SOLUTION: Find the unit rate for the tires at regular price.
SOLUTION: a. Think of 1 hour, 18 minutes and 27 seconds as a
+ sum of 1 +
.
Find the unit rate for the tires at the price advertised
for the manager’s special.
The average speed of the record winner of the
wheelchair division is about 20.04 miles per hour.
b. Divide the distance by the average speed to find
the time.
≈ 1.4970 hours
So, it would take this competitor about 1.5 hours to
complete a 30-mile race.
ANSWER: a. 20.04 mi/h
b. about 1.5 h
10. At Tire Depot, a pair of new tires sells for $216. The
manager’s special advertises the same tires selling at
a rate of $380 for 4 tires. How much do you save per
tire if you purchase the manager’s special?
SOLUTION: Find the unit rate for the tires at regular price.
Subtract the unit rate for the tires at the manager’s
special price from the unit rate for the tires at regular
price.
$108 – $95 = $13
You save $13 per tire if you purchase the manager’s
special.
ANSWER: $13
11. Use Math Tools Find examples of grocery item
prices in a newspaper, on television, or on the
Internet. Compare unit prices of two different brands
of the same item. Explain which item is the better
buy.
SOLUTION: Students should find the price of two different brands
of the same item and the net weight of each item. Then students should calculate the unit price to
determine which item is the better buy.
ANSWER: See students’ work.
12. Find the Error Seth is trying to find the unit price
for a package of blank compact discs on sale at 10
for $5.49. Find his mistake and correct it.
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Find the unit rate for the tires at the price advertised
for the manager’s special.
Page 3
ANSWER: Sometimes; a ratio that compares two measurements
Then students should calculate the unit price to
determine which item is the better buy.
ANSWER: 1-1 Rates
See students’ work.
with different units is a rate, such as
12. Find the Error Seth is trying to find the unit price
for a package of blank compact discs on sale at 10
for $5.49. Find his mistake and correct it.
. 14. A rate is a ratio.
SOLUTION: Sample solution: A ratio is a comparison of any two
quantities by division. A rate is a comparison of two
measurements with different units by division.
Therefore, a rate is always a ratio.
ANSWER: Always; every rate is a ratio because it is a
comparison of two quantities by division.
SOLUTION: Sample answer: Seth used the wrong values for the
dividend and the divisor. He should have divided
$5.49 by 10 to get 0.549 or $0.55 each.
ANSWER: Sample answer: He should have divided $5.49 by 10
to get 0.549 or $0.55 each.
Persevere with Problems Determine whether
the statement is sometimes, always, or never
true. Give an example or a counterexample.
13. A ratio is a rate.
SOLUTION: Sample solution: A ratio that compares two
measurements with different units is a rate, such as
. A ratio that compares two numbers or
two measurements with like units is not a rate, such
as
. Therefore, a ratio is sometimes a rate.
15. Justify Conclusions A 96-ounce container of
orange juice costs $4.80. At what price should a 128ounce container be sold in order for the unit rate for
both containers to be the same? Explain your
reasoning. SOLUTION: Determine the unit rate for the 96-ounce container.
Then, multiply the unit rate by 128 to find the cost of
the other container.
The 128-ounce container would be $6.40.
ANSWER: $6.40; Sample answer: The unit rate for the 96-oz
container is $0.05 per ounce. So, 128 ounces
would cost $0.05 x 128 or $6.40.
Find the unit rate. Round to the nearest
hundredth if necessary.
16. 150 people for 5 classes
SOLUTION: ANSWER: Sometimes; a ratio that compares two measurements
with different units is a rate, such as
. 14. A rate is a ratio.
SOLUTION: Sample solution: A ratio is a comparison of any two
quantities by division. A rate is a comparison of two
measurements with different units by division.
Therefore, a rate is always a ratio.
ANSWER: Always; every rate is a ratio because it is a
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comparison of two quantities by division.
15. Justify Conclusions A 96-ounce container of
The unit rate is 30 people per class.
ANSWER: 30 people per class
17. 815 Calories in 4 servings
SOLUTION: Page 4
The unit rate is 30 people per class.
ANSWER: 1-1 Rates
30 people per class
17. 815 Calories in 4 servings
SOLUTION: The unit rate is 203.75 Calories per serving.
ANSWER: 203.75 Calories per serving
18. $1.12 for 8.2 ounces
SOLUTION: The unit rate is 32 miles per gallon.
ANSWER: 32 mi/gal
20. Justify Conclusions A grocery store sells a 6-pack
of bottled water for $3.79, a 9-pack for $4.50, and a
12-pack for $6.89. Which package costs the least per
bottle? Explain your reasoning.
SOLUTION: Find the unit rate for each package.
6-pack for $3.79
$3.79 ÷ 6 bottles ≈ $0.6317 per bottle
9-pack for $4.50
$4.50 ÷ 9 bottles = $0.50 per bottle
12-pack for $6.89
$6.89 ÷ 12 bottles ≈ $0.5742 per bottle
$0.50 < $0.57 < $0.63
The 9-pack for $4.50 costs the least per bottle.
ANSWER: 9-pack for $4.50; $0.50 < $0.57 < $0.63
21. Justify Conclusions Dalila earns $108.75 for
working 15 hours as a holiday helper wrapping gifts.
At this rate, how much money will she earn if she
works 18 hours the next week? Explain.
The unit rate is about $0.14 per ounce.
ANSWER: $0.14/oz
SOLUTION: Find the unit rate. Then multiply by 18 to find how
much money Dalila will earn in 18 hours.
19. 144 miles on 4.5 gallons
SOLUTION: Since Dalila earns $7.25 per hour, will earn $7.25 × 18 or $130.50 if she works 18 hours the next week.
The unit rate is 32 miles per gallon.
ANSWER: 32 mi/gal
20. Justify Conclusions A grocery store sells a 6-pack
of bottled water for $3.79, a 9-pack for $4.50, and a
12-pack for $6.89. Which package costs the least per
bottle? Explain your reasoning.
SOLUTION: Find the unit rate for each package.
6-pack for $3.79
$3.79 ÷ 6 bottles ≈ $0.6317 per bottle
9-pack for $4.50
$4.50 ÷ 9 bottles = $0.50 per bottle
12-pack for $6.89
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$6.89 ÷ 12 bottles ≈ $0.5742 per bottle
$0.50 < $0.57 < $0.63
The 9-pack for $4.50 costs the least per bottle.
ANSWER: $130.50; $108.75 ÷ 15 = $7.25; $7.25 × 18 = $130.50
22. Use Math Tools Use the graph that shows the
average number of heartbeats for an active adult
brown bear and a hibernating brown bear.
Page 5
ANSWER: $130.50; $108.75 ÷ 15 = $7.25; $7.25 × 18 = $130.50
Use Math Tools Use the graph that shows the
22. Rates
1-1
average number of heartbeats for an active adult
brown bear and a hibernating brown bear.
The bear’s average heart rate when hibernating is 12
beats per minute.
ANSWER: a. The bear’s heart beats 120 times in 2 minutes
when it is active.
b. the bear’s heart rate in beats per minute
c. active: 60 beats per minute; hibernating: 12 beats
per minute
23. The table shows the number of hours a group of
friends worked doing various jobs and the amount
each earned. Select the correct hourly rate to
complete the table. Then place a checkmark in the
row for the person who had the greatest hourly rate.
a. What does the point (2, 120) represent on the
graph?
b. What does the ratio of the y-coordinate to the xcoordinate for each pair of points on the graph
represent?
c. Use the graph to find the bear’s average heart
rate when it is active and when it is hibernating.
SOLUTION: a. On the graph, the point (2, 120) shows that the
bear’s heart beats 120 times in 2 minutes when it is
active.
b. The ratio of the y-coordinate to the x-coordinate
represents the bear’s heart rate in beats per minute.
c. Find the unit rate for the active bear.
SOLUTION: Determine the earnings per hour by dividing the
amount earned by the hours worked.
Caleb: Jeremy: Maria: Rosa: So, Jeremy had the greatest hourly rate.
The bear’s average heart rate when active is 60
beats per minute.
Find the unit rate for the hibernating bear.
ANSWER: The bear’s average heart rate when hibernating is 12
beats per minute.
ANSWER: a. The
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bear’s
heart by
beats
120 times in 2 minutes
when it is active.
b. the bear’s heart rate in beats per minute
24. Mrs. Ross needs to buy dish soap. There are four
differently sized containers. Sort the brands from
least to greatest unit price. Round each unit price to
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the nearest thousandth.
Spotless Soap is the best buy.
1-1 Rates
24. Mrs. Ross needs to buy dish soap. There are four
differently sized containers. Sort the brands from
least to greatest unit price. Round each unit price to
the nearest thousandth.
Which brand is the best buy?
Solve. Write in simplest form.
25. SOLUTION: ANSWER: SOLUTION: Find the unit rate of each brand.
Lots of Suds:
$0.98 ÷ 8 oz = $0.1225 per ounce
Bright Wash:
$1.29 ÷ 12 oz = $0.1075 per ounce
Spotless Soap:
$3.14 ÷ 30 oz ≈ $0.1047 per ounce
Lemon Bright:
$3.45 ÷ 32 oz = $0.1078 per ounce
Spotless Soap costs the least per ounce, so it is the
best buy.
ANSWER: Spotless Soap is the best buy.
Solve. Write in simplest form.
25. SOLUTION: eSolutions Manual - Powered by Cognero
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