Ratios
1. If the ratio of 3a to 7b is 1 to 7, what is the ratio of 6a to
7b?
A) 1 to 14
B) 1 to 35
C) 2 to 7
D) 2 to 21
E) 3 to 7
2. The ratio of a side of square A to the length of rectangle B is
2:3. The ratio of a side of square A to the width of rectangle
B is 2:1. What is the ratio of the area of square A to the
area of rectangle B?
F) 2:1
G) 3:1
H) 3:2
I)
4:1
J) 4:3
3. The ratio of a to b is 3 to 1, and the ratio of b to c is 1 to 5.
2𝑎+3𝑏
What is the value of
?
4𝑏+3𝑐
A) 3/16
B) 9/19
C) 1/2
D) 5/7
E) 18/19
4. Janelle cut a board 30 feet long into 2 pieces. The ratio of
the lengths of the 2 pieces is 2:3. What is the length, to the
nearest foot, of the shorter piece?
F) 5
G) 6
H) 12
I)
15
J) 18
5. Jerome, Kevin, and Seth shared a submarine sandwich.
Jerome ate ½ of the sandwich. Kevin ate 1/3 of the
sandwich, and Seth ate the rest. What is the ratio of
Jerome’s share to Kevin’s share to Seth’s share?
A) 2:3:6
B) 2:6:3
C) 3:1:2
D) 3:2:1
E) 6:3:2
6. Only tenth-, eleventh-, and twelfth-grade students attend
Park City High School. The ratio of tenth graders to the
school’s total student population is 86:255, and the ratio of
eleventh graders to the school’s total population is 18:51.
If 1 student is chosen from random from the entire school,
which grade is that student most likely to be in?
A) Tenth
B) Eleventh
C) Twelfth
D) All grades equally likely
E) Cannot be determined
from the given
information
- 2 - Supplemental Math
© 2017 Breakaway Prep
Rates
7. Stacey usually runs 10 kilometers in a 50-minute run, but
she wants to increase her distance. If she increases the
distance she runs in 50 minutes by s kilometers, what is a
general formula for her new average rate of speed for the
50-minute run, in kilometers per minute?
A)
10
50
B)
50+𝑠
10
C)
50
10+𝑠
D)
10+𝑠
50
E)
10
50+𝑠
8. How many minutes would it take a train to travel 90
kilometers at a constant speed of 120 kilometers per hour?
F)
G)
H)
I)
J)
30
40
45
80
90
9. Ms. Lewis plans to drive 900 miles to her vacation
destination, driving an average of 50 miles per hour. How
many miles per hour faster must she average, while driving,
to reduce her total driving time by 3 hours?
A)
B)
C)
D)
E)
5
8
10
15
18
10. A stone is a unit of weight equivalent to 14 pounds. If a
person weighs 177 pounds, how many stone, to the nearest
tenth, does this person weigh?
A)
B)
C)
D)
E)
247.8
126.4
79.1
12.6
7.9
© 2017 Breakaway Prep Utah, LLC
+ 𝑠
Supplemental Math - 3 -
11. The specific gravity of a substance is the ratio of the weight
of the substance to the weight of an equal volume of water.
If 1 cubic foot of water weighs 62.5 pounds, what is the
specific gravity of a liquid that weighs 125 pounds per cubic
foot?
12. A speedboat traveling in still water at a rate of 30 miles per
hour takes ½ hour to reach an island. If the boat traveled at
a rate of 3 miles per hour over the same route, how many
hours would the trip take?
A)
B)
C)
D)
E)
1
1.25
2
6.25
125
F) 0.05
G) 5
H) 10
I)
15
J) 45
Answer Key
Ratios
Rates
- 4 - Supplemental Math
1
2
3
4
5
6
7
8
9
10
11
12
C
J
B
H
D
B
D
H
C
D
C
G
© 2017 Breakaway Prep