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Solving Mixture Problems Answers

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1
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A ride on the roller coaster costs 4 tickets while the boat ride only costs 3 tickets. Michael went on the two rides a total of 10 times and spent a total of 37 tickets.

Question illustration
A
r(10 – r) = 10
B
r + (10 – r) = 4 + 3
C
4r[3(10 – r)] = 37
D
4r + 3(10 – r) = 37
2
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Giuliana has 22 quarters and dollar coins worth a total of $10.75.

A
d – 22 + 0.25d = 10.75
B
0.25d + 22 – d = 10.75
C
0.25(22 – d) + d = 10.75
D
d + 0.25(d – 22) = 10.75
3

A snack cart sells lemonade for $2 and hot dogs for $5. The vendor sold 86 items today for a total of $330.

Question illustration
A
(86 – h)(h) = 86
B
(86 – h) + h = 86
C
(86 – h) + h = 2 + 5
D
[2(86 – h)](5h) = 330
4

Shelby mixes a 25% bleach solution with 5 cups of a 10% bleach solution, resulting in a 20% bleach solution. The table shows the amount of each solution used.What is the value of x?

Question illustration
A
1
B
3
C
10
D
24
5

Students are given 3 minutes to complete each multiple-choice question on a test and 8 minutes for each free-response question. There are 15 questions on the test and the students have been given 55 minutes to complete it.Which value could replace x in the table?

Question illustration
A
7 – m
B
23 – m
C
8(15 – m)
D
8(15) – m
6

The hardcover version of a book weighs 7 ounces while its paperback version weighs 5 ounces. Forty-five copies of the book weigh a total of 249 ounces.Which value could replace x in the table?

Question illustration
A
40 – h
B
50 – h
C
5(45) – h
D
5(45 – h)
7

Maki uses 20 gallons of a solution with an unknown ethanol concentration and 60 gallons of a 12% ethanol solution to make 80 gallons of a 10% solution. The table shows the amount of each solution.What is the value of x, the concentration of the unknown ethanol solution?

Question illustration
A
0.02
B
0.04
C
0.05
D
0.08
8

A chemist mixes 4 liters of one acid solution with 10 liters of a 40% solution, resulting in a 30% acid solution. The table shows the amount of each solution used.What is the value of x, the acid concentration of the first solution?

Question illustration
A
0.05
B
0.10
C
0.15
D
0.20
9

Milk and cream are mixed together for a recipe. The total volume of the mixture is 1 cup. If the milk contains 2% fat, the cream contains 18% fat, and the mixture contains 6% fat, how much cream is in the mixture?

A
cup
Option A
B
cup
Option B
C
cup
Option C
D
cup
Option D
10

A collection of 108 coins containing only quarters and nickels is worth $21.

Question illustration
A
21
B
108
C
21 – n
D
108 – n
11

A restaurant freezes a cherry and lime juice mixture to create slushes. Cherry juice costs $5 per quart, and lime juice costs $3 per quart. Each day, the restaurant spends a total of $36 on 8 quarts of juice. The restaurant manager organizes the information in the table below.Which equation can be used to determine the amount of cherry juice in each mixture?

Question illustration
A
5q + 3(8 – q) = 36
B
5q + 3(8 – q) = 8
C
q + (8 – q) = 8
D
q + 5 = 5q
12

Milk and cream are mixed together for a recipe. The total volume of the mixture is 1 cup. If the milk contains 2% fat, the cream contains 18% fat, and the mixture contains 6% fat, how much cream is in the mixture?

A
cup
Option A
B
cup
Option B
C
cup
Option C
D
cup
Option D
13

Students are given 3 minutes to complete each multiple-choice question on a test and 8 minutes for each free-response question. There are 15 questions on the test and the students have been given 55 minutes to complete it.Which value could replace x in the table?

Question illustration
A
7 – m
B
23 – m
C
8(15 – m)
D
8(15) – m
14

A chemist mixes 4 liters of one acid solution with 10 liters of a 40% solution, resulting in a 30% acid solution. The table shows the amount of each solution used.What is the value of x, the acid concentration of the first solution?

Question illustration
A
0.05
B
0.10
C
0.15
D
0.20
15

Giuliana has 22 quarters and dollar coins worth a total of $10.75.

A
d – 22 + 0.25d = 10.75
B
0.25d + 22 – d = 10.75
C
0.25(22 – d) + d = 10.75
D
d + 0.25(d – 22) = 10.75
16

Dr. Bhatia mixes 2 liters of a 5% saline solution with x liters of a 9% saline solution. The table shows the amount of each solution used.

Question illustration
A
3
B
4
C
5
D
6
17

Fifteen percent of the pigment in paint color A is black. Sixty percent of the pigment in paint color B is black. An unknown amount of paint color B is mixed with 40 ml of paint color A, resulting in a paint that contains 25% black pigment.Which equation can be used to solve for x, the total amount of paint in the mixture of the two colors?

A
0.15(40) + 0.6x = 0.25(40 + x)
B
0.15(40) + 0.6(x – 40) = 0.25(x)
C
0.15(40) + 0.6x = 0.25(40 – x)
D
0.15(40) + 0.6(x + 40) = 0.25(x)
18

A snack cart sells lemonade for $2 and hot dogs for $5. The vendor sold 86 items today for a total of $330.

Question illustration
A
(86 – h)(h) = 86
B
(86 – h) + h = 86
C
(86 – h) + h = 2 + 5
D
[2(86 – h)](5h) = 330
19

Maki uses 20 gallons of a solution with an unknown ethanol concentration and 60 gallons of a 12% ethanol solution to make 80 gallons of a 10% solution. The table shows the amount of each solution.What is the value of x, the concentration of the unknown ethanol solution?

Question illustration
A
0.02
B
0.04
C
0.05
D
0.08
20

A 4% peroxide solution is mixed with a 10% peroxide solution, resulting in 100 L of an 8% solution. The table shows the amount of each solution used in the mixture.

Question illustration
A
6
B
7
C
8
D
9

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