Free Printable Writing Systems of Equations from Word Problems

1.

Michael spent $50 for 6 tigerfish and 8 goldfish. Shaun spend $5 more than Michael for 5 tigerfish and 10 goldfish. Write a system of equations that could be use the find t, the price of a tigerfish and g, the price of a goldfish.

a)

$8t+6g=50$
$10t+5g=55$

b)

$6t+8g=50$
$5t+10g=45$

c)

$6t+8g=50$
$5t+10g=55$

d)

$8t+6g=50$
$10t+5g=45$

2.

Sarah enjoys cutting lawns and charges $20 for each small lawn and $30 for each large lawn she mows. Sarah earned $140 for mowing 6 lawns. Write a system of equations that could be used to find x, small lawns and y, large lawns Sarah mowed.

a)

$30x+20y=140$
$x+y=6$

b)

$50\left(x+y\right)=140$
$x+y=6$

c)

$20x+30y=140$
$x+y=6$

d)

$x+y=140$
$x+y=6$

3.

The length of a rectangular playground is 4 meters less than 3 times the width. The perimeter is 64 meters. Write a system of equations that could be used to find l, the length and w, the width of the rectangular playground.

a)

$l=3w-4$
$2l+2w=64$

b)

$l=3w-4$
$l+w=64$

c)

$l=4-3w$
$2l+2w=64$

d)

$l=4-3w$
$l+w=64$

4.

The drama club is selling tickets to its play. The cost of an adult ticket is $4.50, and the cost of a student ticket is $2.50. The theater can hold 250 people and they want to make $1,005. Write a system of equations that could be used to find x, the number of adult tickets and y, the number of student tickets.

a)

$4.50x+2.50y=1,005$
$x+y=250$

b)

$4.50x+2.50y=250$
$x+y=1,005$

c)

$2.50x+4.50y=1,005$
$x+y=250$

d)

$2.50x+4.50y=250$
$x+y=1,005$

5.

Kacey is thinking of two numbers. Their sum is -18. Their difference is 38. Write a system of equations that could be used to find the two numbers.

a)

$x+y=-18$
$x-y=38$

b)

$x-y=-18$
$x+y=38$

c)

$x\cdot y=-18$
$x\div y=38$

d)

$x\div y=-18$
$x\cdot y=38$

6.

The Spanish Club is selling tacos for a fundraiser. One student sold 12 chicken tacos and 15 beef tacos and raised $61.23. Another student raised $13.45 more than the first student by selling 10 chicken tacos and 22 beef tacos. Write a system of equations that could be used to find c, the price of chicken tacos and b, the price of beef tacos sold in the fundraiser.

a)

$12c+15b=61.23$
$10c+22b=47.78$

b)

$12c+15b=61.23$
$10c+22b=74.68$

c)

$15b+12c=61.23$
$22c+10b=74.68$

d)

$15b+12c=61.23$
$22c+10b=47.78$

7.

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings (x) when both companies cost (y) the same amount?

a)

y = 6.80 + .65x

y=7.30+.90x

b)

x + y = 6.80

x + y = 7.30

c)

y = 6.80+.90x

y = 7.30 + .65x

d)

y + .90x = 6.80

y + .65x = 7.30

8.

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

a)

t: # of tacos
m: # of glasses of milk

b)

t: Cost of each taco
m: Cost of each glass of milk

c)

t: total cost
m: # of food items

d)

t: Cost of each glass of milk
m: Cost of each taco

9.

There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Which system of equations best represents the situation?

a)

h + c = 15

4h + 2c = 44

b)

4h + 2c= 15

h + c = 44

c)

h = 2c + 44

4h = c + 15

d)

2h - 4c = 44

h - c = 15

10.

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

a)

S + A = 530

3S + 4A = 1740

b)

S + A = 530

4S + 3A = 1740

c)

S + A = 1740

3S + 4A = 530

d)

S + A = 1740

4S + 3A = 530

11.

Caitlin won a bag full of money at the fundraiser party! She won 49 bills that amounted to $1430. The bills consist of twenty dollar bills and fifty dollar bills. Using x for number of $20 bills and y for number of $50 bills, which systems would help determine how many of each bill Caitlin has?

a)

x + y = 1430

20x + 50y = 49

b)

x + y = 49

10x + 5y = 1430

c)

x + y = 49

20x + 50y = 1430

d)

x + y = 49

x + y = 1430

12.

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years.

If x=Erin's age and y=Alex's age, choose the system that matches the situation.

a)

x + y = 33

y = 2x - 3

b)

x + y = 33

x = 2y - 3

c)

x + y = 33

x = 3 - 2y

d)

x + y = 3

x = 33 - 2y

13.

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which two equations can you use to determine how many sodas and nachos David sold if n represents number of nachos and s represents number of sodas?

a)

n + s = 87

b)

n + s = 78.50

c)

1.50n + 0.50s = 78.50

d)

1.50n + 0.50s = 87

14.

The seniors of Central High School and North High school are planning trips to Yellowstone National Park. Central filled 8 vans and 3 buses with 208 students. North filled 14 vans and 12 buses with 580 students. Each van and each bus carried the same number of students. Select the two equations you can use to determine how many students were in each van (v), and how many in each bus (b)?

a)

14v + 12b = 580

b)

8v + 3b = 208

c)

8v + 12b = 208

d)

12v + 14b = 580

e)

3v + 8b = 208

15.

A test has twenty questions worth 100 points. The test consists of multiple choice questions (m) worth 3 points each and written response questions (w) worth 11 points each. Which two equations can you use to help determine how many of each question type are on the test?

a)

m + w = 20

b)

m + w = 100

c)

3m + 11w = 20

d)

3m + 11w = 100

Writing Systems of Equations from Word Problems

Total questions: 15

Worksheet time: 2hrs 35mins

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