Ratios and Rates
Claire has 6 large envelopes and 11 small envelopes. What is the ratio of large envelopes to the total number of envelopes?
A 5 : 11 B 6 : 11
C 6 : 17 D 11 : 17
C 6 : 17
Jake takes guitar lessons that cost $120 per month. Which equation can be used to determine the total number of dollars, d , that Jake pays for lessons for any number of months, m?
A d = 120 x m B m = 120 x d
C d = 120 + m D m = 120 + d
A d = 120 x m
dollars (cost of lessons) = $120 x m (for every month)
What is the value of the expression shown below when x = 7?
3x2 - 2x + 3
A 31 B 50
C 136 D 164
3x2 - 2x + 3
3(72) - 2(7) + 3
3(49) - 2(7) + 3
147 - 14 + 3
133 + 3
136
A group of 10 Science Club students is on a field trip. That number of students represents 20% of the total number of students in the Science Club. What is the total number of students in the Science Club?
A 20 B 30
C 50 D 80
C 50
Three vertices of a rectangle are located at (2, 4), (-2, -5), and (-2, 4) on a coordinate plane. What are the coordinates of the fourth vertex of the rectangle?
A (2, 5) B (2, −5)
C (5, 2) D (−5, −2)
B (2, -5)
Ms. Wilson is buying packages of pencils. Each package costs $11.52 and contains 96 pencils. What is the unit price of a pencil?
A $0.12 B $0.96
C $1.20 D $1.92
A $0.12
Johnny is 21 years old. He is 3 times as old as Becky. Write and solve an equation to determine Becky’s age, a.
3a = 21
21 = 3a
21/3 = a
Which value of x makes the equation true?
4x - 8 = 4
A 1 B 3
C 4 D 9
4x - 8 = 4
4(3) - 8 = 4
12 - 8 = 4
4 = 4
There was a total of 640 students at a school on Friday. Every student either walked or rode in a bus to the school. If 45% of the total number of students walked to the school on Friday, how many of the students rode in a bus to the school?
A 288 B 352
C 585 D 595
B 352
The outside temperature in a town is -20 degrees Fahrenheit. What change in temperature, in degrees Fahrenheit, would bring the outside temperature to 0 degrees Fahrenheit?
A −21 B −20
C 0 D 20
D 20
There are red tiles and blue tiles in a box. The ratio of red tiles to blue tiles is 3 : 5. There are 12 more blue tiles than red tiles in the box. How many red tiles are in the box?
A 18 B 20
C 30 D 48
3 : 5
6 : 10
9 : 15
12 : 20
15 : 25
18: 30 30-18=12 A 18
An office supply store sells boxes of pencils. Each box contains 160 pencils. Write an equation that represents the total number of pencils, y , in x boxes.
y = 160x
160x = y
Josh has c coins. Nick has 4 fewer than 3 times as many coins as Josh. Which expression can be used to show how many coins Nick has?
A 3c − 4 B 3 − 4c
C 4c − 3 D 4 − 3c
A 3c - 4
The number 60 is 75% of what number?
A 45 B 80
C 120 D 125
B 80
A restaurant owner orders new plates and spoons based on the following: plates are sold in packages of 9 and spoons are sold in packages of 12. The restaurant owner orders an equal number of plates and spoons. What is the least number of packages of plates and packages of spoons she should order to have an equal number of plates and spoons?
plates spoons 4 packages of plates and
9 12 3 packages of spoons
18 24
27 36
36
The ratio of number of yards to number of miles is 3,520 : 2. How many yards are in 5 miles?
A 1,760 B 5,280
C 7,040 D 8,800
D 8,800
A bakery owner bakes 450 cookies each day. Which equation can be used to determine the number of cookies, c , the owner bakes for any number of days, d?
A c = d + 450 B d = c + 450
C 450d = c D 450c = d
C 450d = c
450 cookies per day
450 cookies times the number of day = the total number of cookies
A student evaluates the expression 17(4 + 15) by
adding the product of 17 and 4 to the product of
17 and 15. Is the student correct? Why or why not?
The student is correct because the distributive property was applied. 17(4) + 17(15)
An ice cream shop sold 48 vanilla milkshakes in a day, which was 40% of the total number of milkshakes sold that day. What was the total number of milkshakes that the ice cream shop sold that day?
A 60 B 72
C 100 D 120
D 120
What is the least common multiple of 9 and 12 ?
A 3
B 36
C 72
D 108
B 36
Mark ran 8 miles in 60 minutes. If Mark continues to run at that same rate, how many minutes will it take him to run 12 miles?
A 48 B 72
C 90 D 96
C 90
Which expression is equivalent to 8(2a + 3b) - 2b?
A 16a + b B 16a + 8b
C 16a + 22b D 16a + 24b
8(2a + 3b) - 2b
16a + 24b - 2b
16a + 22b
C
Which expression is equivalent to 14 less than the product of 8 and y?
A 14 - 8y B 14 - y/8
C 8y - 14 D y/8 - 14
C 8y - 14
A restaurant used 231 eggs last week. Of these, 46 were brown in color. The remaining eggs were white in color. Which equation can be used to solve for w, the number of white eggs used last week?
A 231 + 46w = 0 B 46 + w = 231
C w = 231 + 46 D 231 = 46w
B 46 + w = 231
46 brown + w white = 231 total eggs used
Which set of values makes the inequality n is greater than or equal to -5 true?
A {-5, -5.5, -6} B {-5, -4.5, -3}
C {-6, 0, 5} D {-6, -7, -8}
B -5, -4.5, and -3 are all greater than or equal to -5.
Picture the number line
-5 -4 -3 -2 -1 0 1 2 3 4 5