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Problem Solving
7-2 Ratios, Rates, and Unit Rates
Scientists have researched the ratio of brain weight to body
size in different animals. The results are in the table below.
1. Order the animals by their brain
Animal
weight to body weight ratio, from
smallest to largest.
Cat
Dog
Elephant
2. It has been hypothesized that the
higher the brain weight to body weight
ratio, the more intelligent the animal
is. By this measure, which animals
listed are the most intelligent?
Hippo
Horse
Human
Small birds
3. Name two sets of animals that have
approximately the same brain weight
to body weight ratio.
Brain Weight
!!
Body W e ight
1
!!
100
1
!!
125
1
!!
560
1
!!
2789
1
!!
600
1
!!
40
1
!!
12
Find the unit rate. Round to the nearest hundredth.
4. A 64-ounce bottle of apple juice
costs $1.35.
A $0.01/oz
C $0.47/oz
D $47.4/oz
B $0.02/oz
5. Find the unit rate for a 2 lb package
of hamburger that costs $3.45.
F $0.58/lb
H $1.73/lb
G $1.25/b
J $2.28/b
6. 12 slices of pizza cost $9.00.
A $0.45/slice
C $0.75/slice
B $0.50/slice
D $1.33/slice
7. John is selling 5 comic books
for $6.00.
F $0.83/book
H $1.02/book
J $1.45/book
G $1.20/book
8. There are 64 beats in 4 measures
of music.
A 16 beats/measure
B 12 beats/measure
C 4 beats/measure
D 0.06 beats/measure
9. The average price of a 30 second
commercial for the 2002 Super Bowl
was $1,900,000.
F $120.82/sec
G $1,242.50/sec
H $5,839.02/sec
J $63,333.33/sec
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22
Holt Middle School Math
MSM04G8_RESBK_Ch07_102-122
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7-2 Ratios, Rates, and Unit Rates
LESSON
LESSON
7-2 Ratios, Rates, and Unit Rates
A rate is a ratio that compares two different kinds of quantities.
Find each unit rate.
1. 4860 mi in 15 days
2. $15 for 3 hours
324 mi per day
3. $3.90 for 10 lb of
oranges
$5 per hour
4. 630 desks in 18 rooms
5. 320 mi on 16 gal of
gasoline
35 desk per room
135 words in 3 minutes
7 ads per 4 pages of copy
2 aides
!!
18 students
135 words
!!
3 minutes
7 ads
!!
4 pages of copy
$0.39 per pound
6. 576 heartbeats in 8 min
20 mi per gallon
7. 1170 mi in 18 hours
2 aides for 18 students
72 beats per minute
Express each comparison as a rate in ratio form.
1. 275 students per
11 teachers
19 students per room
68 words per minute
Find each unit price and tell which is the better buy.
15 strike-outs
!!
6 innings
In a unit rate, the second quantity is 1.
300 miles in 6 hours
10. 3 lb beef roast for $8.97; 5 lb beef roast for $14.85
81 entries in 4 minutes
300 miles
300 " 6
50 miles
!! ! !! ! !!
6 hours
6"6
1 hour
3 lb unit price is $2.99; 5 lb unit price is $2.97; better buy is
81 entr ies
81 " 4
20.25 entries
!! ! !! ! !!
4 minu tes
4"4
1 minute
Express each comparison as a unit rate.
5 lb for $14.85
4. 28 patients for 2 nurses
11. 3 dozen binder clips for $2.88; 72 binder clips for $5.40
the better buy is 72 clips for $5.40
2.3 children
16 children
16 " 7
! ! ! !! ! ! !
7 families
7"7
1 family
A unit price tells the price per 1 unit.
12. 14.5 gallons of gasoline for $18.56; 18.6 gallons for $23.25
14.5 gallons unit price is $1.28; 18.6 gallons unit price is $1.25;
better buy is 18.6 gallons for $23.25
13. Mr. Acito takes his students on a field trip to the theater.
As the teacher, his ticket is free, but he is charged $472 for his
32 students. What is the price per ticket for each student?
$2.49 for 3 muffins
$1.67 for 10 pencils
$2.49
$0.83
2.49 " 3
!! ! !! ! !!
3 muffins
1 muffin
3"3
$1.67
$0.167
1.67 " 10
!! ! !! ! !!
10 pencils
1 pencil
10 " 10
$0.83 for 1 muffin
$0.17 for 1 pencil
Find each unit price.
6. $10.74 for
3 reams of paper
$14.75 a ticket
14. A company is charged $11,460 a year for an advertisement that
appears in the telephone directory. What is the charge per
month for the ad?
$10.74
10.74 " 3
!! ! !!
3 reams
3"3
7. $9.99 for 6 blank
jewel cased CDs
$9.99
9.99 " 6
!! ! !!
6 CDs
6"6
$3.58
!!
1 ream
$955 per month
19
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
5. 16 children in 7 families
14 patients
28 pa tients
28 " 2
! ! ! !! ! !!
2 nur ses
2"2
1 nurse
3 dozen clips unit price is $0.08; 72 clips unit price is $0.075;
Holt Pre-Algebra
Challenge
7-2 All That Glitters
8. $8.99 for a 12-pack
of gel pens
$8.99
8.99 " 12
!! ! !!
12 pens
12 " 12
$1.665
!!
1 CD
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
$0.7492
!!
1 pen
20
Holt Pre-Algebra
Problem Solving
7-2 Ratios, Rates, and Unit Rates
LESSON
LESSON
Used by the ancient Greeks around 500 B.C., the golden rectangle
is thought to have a shape that is most pleasing to the human eye.
Scientists have researched the ratio of brain weight to body
size in different animals. The results are in the table below.
1. Order the animals by their brain
Animal
weight to body weight ratio, from
smallest to largest.
Cat
Follow these steps to construct a golden rectangle to determine its
dimensions.
1. a. Work with square ABCD below of side 2 inches.
Use a ruler to locate M, the midpoint of A
!B
!.
b. Draw M
!C
!. Use the Pythagorean theorem to find MC.
!" so that MP ! MC.
c. Extend !
AB
! through B. Locate P on AB
hippo, horse, elephant, dog,
AM !
1
MC !
"5
!
AP !
1 # "5
!
2 in.
C
Dog
cat, human, small birds
!".
d. Extend !
DC
! through C. At P, draw a line perpendicular to AB
!".
Use Q to label the point at which the perpendicular intersects DC
APQD is a golden rectangle.
D
3. 15 strike-outs in
6 innings
3 books
!!
2 months
275 students
!!
11 teachers
8. 285 students in 15 rooms 9. 2380 words in 35 min
65 mi per hour
2. 3 books in 2 months
Elephant
2. It has been hypothesized that the
higher the brain weight to body weight
ratio, the more intelligent the animal
is. By this measure, which animals
listed are the most intelligent?
Hippo
Horse
Human
small birds
Q
Small birds
3. Name two sets of animals that have
approximately the same brain weight
to body weight ratio.
Brain Weight
!!
Body W e ight
1
!!
100
1
!!
125
1
!!
560
1
!!
2789
1
!!
600
1
!!
40
1
!!
12
elephant and horse; cat & dog
2 in.
Find the unit rate. Round to the nearest hundredth.
A
M
B
P
AP
! is called the golden ratio.
2. In golden rectangle APQD, the ratio !
AD
a. The exact value of the golden ratio is:
b. Write an approximation of the golden ratio.
Use as many decimal places as your calculator allows.
3. a. Write the reciprocal of the golden ratio.
b. Write an approximation of
the reciprocal of the golden ratio.
!
1 # "5
!!
2
4. A 64-ounce bottle of apple juice
costs $1.35.
A $0.01/oz
C $0.47/oz
D $47.4/oz
B $0.02/oz
!
5. Find the unit rate for a 2 lb package
of hamburger that costs $3.45.
F $0.58/lb
H $1.73/lb
!
G $1.25/b
J $2.28/b
6. 12 slices of pizza cost $9.00.
A $0.45/slice
C $0.75/slice
!
B $0.50/slice
D $1.33/slice
7. John is selling 5 comic books
for $6.00.
F $0.83/book
H $1.02/book
J $1.45/book
G $1.20/book
!
8. There are 64 beats in 4 measures
of music.
A 16 beats/measure
!
B 12 beats/measure
C 4 beats/measure
D 0.06 beats/measure
9. The average price of a 30 second
commercial for the 2002 Super Bowl
was $1,900,000.
F $120.82/sec
G $1,242.50/sec
H $5,839.02/sec
J $63,333.33/sec
!
1.6180339887
2
!!
!
1 # "5
0.6180339887
c. Comment on the result.
Decimal portions of golden ratio and its reciprocal are the same.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
21
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Pre-Algebra
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
105
22
Holt Pre-Algebra
Holt Middle School Math