Math Practice Problems - Mixture Word Problems

Mixture Word Problems - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

Learn more about our online math practice software.
See some of our other supported math practice problems.

Complexity=1, Mode=tickets

A ticket booth sold 226 tickets and collected $843 in ticket sales. Adult tickets are $5.50 and child tickets are $1.50. How many tickets of each type were sold?
Adult: tickets Child: tickets

A ticket booth sold 290 tickets and collected $2381 in ticket sales. Adult tickets are $10 and child tickets are $7. How many tickets of each type were sold?
Adult: tickets Child: tickets

Complexity=1, Mode=soln

You have 18 milliliters of a 45% alcohol solution. How many milliliters of a 51% alcohol solution needs to be added to make a 49% alcohol solution?
milliliters

You have 4 liters of a 30% alcohol solution. How many liters of pure water needs to be added to make a 5% alcohol solution?
liters

Complexity=1, Mode=food

You make a new nut mixture by adding 12 pounds of cashews that cost $9.07/lb and 6 pounds of peanuts that cost $8.17/lb. What is the price of your new nut mixture?
$ / lb

You make a new bean mixture by adding 15 pounds of pinto beans that cost $9.22/lb and 3 pounds of black beans that cost $5.80/lb. What is the price of your new bean mixture?
$ / lb

Complexity=1, Mode=mixed

How many pounds of walnuts worth $4.37/lb should be mixed with 4 pounds of pecans worth $3.73/lb to make a mixture worth $4.05/lb?
lb

You have 18 ounces of a 15% alcohol solution. How many ounces of a 19% alcohol solution needs to be added to make a 17% alcohol solution?
ounces

Answers

Complexity=1, Mode=tickets

Problem

Correct Answer

Your Answer

A ticket booth sold 226 tickets and collected $843 in ticket sales. Adult tickets are $5.50 and child tickets are $1.50. How many tickets of each type were sold?

Adult: tickets Child: tickets

Solution

	# Tickets	Price	Ticket Sales
Adult	A	$5.50	($5.50)(A)
Child	226 - A	$1.50	($1.50)(226 - A)
Total	226	----	$843

Equation setup: ($5.50)(A) + ($1.50)(226 - A) = $843

Answer:
A = 126 tickets
226 - A = 100 tickets

Problem

Correct Answer

Your Answer

A ticket booth sold 290 tickets and collected $2381 in ticket sales. Adult tickets are $10 and child tickets are $7. How many tickets of each type were sold?

Adult: tickets Child: tickets

Solution

	# Tickets	Price	Ticket Sales
Adult	A	$10	($10)(A)
Child	290 - A	$7	($7)(290 - A)
Total	290	----	$2381

Equation setup: ($10)(A) + ($7)(290 - A) = $2381

Answer:
A = 117 tickets
290 - A = 173 tickets

Complexity=1, Mode=soln

Problem

Correct Answer

Your Answer

You have 18 milliliters of a 45% alcohol solution. How many milliliters of a 51% alcohol solution needs to be added to make a 49% alcohol solution?

milliliters

Solution

	Amount of solution	% alcohol	Amount of alcohol
51% solution	x	0.51	(0.51)(x)
45% solution	18	0.45	(0.45)(18)
49% mixture	x + 18	0.49	(0.49)(x + 18)

Equation setup: (0.51)(x) + (0.45)(18) = (0.49)(x + 18)
Answer: x = 36 milliliters

Problem

Correct Answer

Your Answer

You have 4 liters of a 30% alcohol solution. How many liters of pure water needs to be added to make a 5% alcohol solution?

liters

Solution

	Amount of solution	% alcohol	Amount of alcohol
pure water	x	0	(0)(x)
30% solution	4	0.3	(0.3)(4)
5% mixture	4 + x	0.05	(0.05)(4 + x)

Equation setup: (0)(x) + (0.3)(4) = (0.05)(4 + x)
Answer: x = 20 liters

Complexity=1, Mode=food

Problem

Correct Answer

Your Answer

You make a new nut mixture by adding 12 pounds of cashews that cost $9.07/lb and 6 pounds of peanuts that cost $8.17/lb. What is the price of your new nut mixture?

$ / lb

Solution

	Pounds	Price/lb	Total Cost
Cashews	12	$9.07	($9.07)(12)
Peanuts	6	$8.17	($8.17)(6)
Mixture	12 + 6	x	(x)(12 + 6)

Equation setup: ($9.07)(12) + ($8.17)(6) = (x)(12 + 6)
Answer: x = $8.77 /lb

Problem

Correct Answer

Your Answer

You make a new bean mixture by adding 15 pounds of pinto beans that cost $9.22/lb and 3 pounds of black beans that cost $5.80/lb. What is the price of your new bean mixture?

$ / lb

Solution

	Pounds	Price/lb	Total Cost
Pinto beans	15	$9.22	($9.22)(15)
Black beans	3	$5.80	($5.80)(3)
Mixture	15 + 3	x	(x)(15 + 3)

Equation setup: ($9.22)(15) + ($5.80)(3) = (x)(15 + 3)
Answer: x = $8.65 /lb

Complexity=1, Mode=mixed

Problem

Correct Answer

Your Answer

How many pounds of walnuts worth $4.37/lb should be mixed with 4 pounds of pecans worth $3.73/lb to make a mixture worth $4.05/lb?

Solution

	Pounds	Price/lb	Total Cost
Walnuts	x	$4.37	($4.37)(x)
Pecans	4	$3.73	($3.73)(4)
Mixture	x + 4	$4.05	($4.05)(x + 4)

Equation setup: ($4.37)(x) + ($3.73)(4) = ($4.05)(x + 4)
Answer: x = 4 lb

Problem

Correct Answer

Your Answer

You have 18 ounces of a 15% alcohol solution. How many ounces of a 19% alcohol solution needs to be added to make a 17% alcohol solution?

ounces

Solution

	Amount of solution	% alcohol	Amount of alcohol
19% solution	x	0.19	(0.19)(x)
15% solution	18	0.15	(0.15)(18)
17% mixture	x + 18	0.17	(0.17)(x + 18)

Equation setup: (0.19)(x) + (0.15)(18) = (0.17)(x + 18)
Answer: x = 18 ounces

Learn more about our online math practice software.

"MathScore works."
- John Cradler, Educational Technology Expert