Math Practice Problems - Mixture Word Problems

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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.

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Complexity=1, Mode=soln

Complexity=1, Mode=food

Complexity=1, Mode=mixed

Answers

Complexity=1, Mode=tickets

Problem

Correct Answer

Your Answer

A ticket booth sold 414 tickets and collected $1931 in ticket sales. Adult tickets are $6.50 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	$6.50	($6.50)(A)
Child	414 - A	$1.50	($1.50)(414 - A)
Total	414	----	$1931

Equation setup: ($6.50)(A) + ($1.50)(414 - A) = $1931

Answer:
A = 262 tickets
414 - A = 152 tickets

Problem

Correct Answer

Your Answer

A ticket booth sold 486 tickets and collected $2416.50 in ticket sales. Adult tickets are $5.50 and child tickets are $4. 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	486 - A	$4	($4)(486 - A)
Total	486	----	$2416.50

Equation setup: ($5.50)(A) + ($4)(486 - A) = $2416.50

Answer:
A = 315 tickets
486 - A = 171 tickets

Complexity=1, Mode=soln

Problem

Correct Answer

Your Answer

You have 25 liters of a 50% soap solution. How many liters of pure water needs to be added to make a 25% soap solution?

liters

Solution

	Amount of solution	% soap	Amount of soap
pure water	x	0	(0)(x)
50% solution	25	0.5	(0.5)(25)
25% mixture	25 + x	0.25	(0.25)(25 + x)

Equation setup: (0)(x) + (0.5)(25) = (0.25)(25 + x)
Answer: x = 25 liters

Problem

Correct Answer

Your Answer

Solution X is a 27% salt solution and Solution Y is a 20% salt solution. How much of each is needed to make 42 gallons of a 25% salt solution?

Solution X: gallons Solution Y: gallons

Solution

	Amount of solution	% salt	Amount of salt
27% solution	x	0.27	(0.27)(x)
20% solution	42 - x	0.2	(0.2)(42 - x)
25% mixture	42	0.25	(0.25)(42)

Equation setup: (0.27)(x) + (0.2)(42 - x) = (0.25)(42)

Answer:
x = 30 gallons
42 - x = 12 gallons

Complexity=1, Mode=food

Problem

Correct Answer

Your Answer

You make a new bean mixture by adding 14 pounds of lima beans that cost $5.51/lb and 14 pounds of pinto beans that cost $4.91/lb. What is the price of your new bean mixture?

$ / lb

Solution

	Pounds	Price/lb	Total Cost
Lima beans	14	$5.51	($5.51)(14)
Pinto beans	14	$4.91	($4.91)(14)
Mixture	14 + 14	x	(x)(14 + 14)

Equation setup: ($5.51)(14) + ($4.91)(14) = (x)(14 + 14)
Answer: x = $5.21 /lb

Problem

Correct Answer

Your Answer

You make 60 pounds of a coffee mixture using Coffee A and Coffee B . Coffee A cost $4.08/lb and Coffee B cost $3.48/lb. How many pounds of each kind of coffee were added if the coffee mixture costs $3.78/lb?

Coffee A: lb Coffee B: lb

Solution

	Pounds	Price/lb	Total Cost
Coffee A	x	$4.08	($4.08)(x)
Coffee B	60 - x	$3.48	($3.48)(60 - x)
Mixture	60	$3.78	($3.78)(60)

Equation setup: ($4.08)(x) + ($3.48)(60 - x) = ($3.78)(60)

Answer:
x = 30 lb
60 - x = 30 lb

Complexity=1, Mode=mixed

Problem

Correct Answer

Your Answer

You have 20 gallons of a 45% antifreeze solution. How many gallons of a 57% antifreeze solution needs to be added to make a 51% antifreeze solution?

gallons

Solution

	Amount of solution	% antifreeze	Amount of antifreeze
57% solution	x	0.57	(0.57)(x)
45% solution	20	0.45	(0.45)(20)
51% mixture	x + 20	0.51	(0.51)(x + 20)

Equation setup: (0.57)(x) + (0.45)(20) = (0.51)(x + 20)
Answer: x = 20 gallons

Problem

Correct Answer

Your Answer

You make a new nut mixture by adding 45 pounds of cashews that cost $6.24/lb and 9 pounds of pecans that cost $3.24/lb. What is the price of your new nut mixture?

$ / lb

Solution

	Pounds	Price/lb	Total Cost
Cashews	45	$6.24	($6.24)(45)
Pecans	9	$3.24	($3.24)(9)
Mixture	45 + 9	x	(x)(45 + 9)

Equation setup: ($6.24)(45) + ($3.24)(9) = (x)(45 + 9)
Answer: x = $5.74 /lb

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