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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=tickets

 1.   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 2.   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

### Complexity=1, Mode=soln

 1 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 2.   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

### Complexity=1, Mode=food

 1 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 2.   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

### Complexity=1, Mode=mixed

 1 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 2 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

### Complexity=1, Mode=tickets

1A 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?
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

 A = 262 tickets 414 - A = 152 tickets

2A 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?
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

 A = 315 tickets 486 - A = 171 tickets

### Complexity=1, Mode=soln

1You 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 ofsolution % soap Amount ofsoap 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)
2Solution 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 ofsolution % salt Amount ofsalt 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)

 x = 30 gallons 42 - x = 12 gallons

### Complexity=1, Mode=food

1You 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)
2You 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)

 x = 30 lb 60 - x = 30 lb

### Complexity=1, Mode=mixed

1You 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 ofsolution % antifreeze Amount ofantifreeze 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)