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WorksheetsSystem of Equations Word Problems
Total questions: 17
Worksheet time: 4hrs 5mins
Name
Class
Date
1.
There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Which system of equations represents the situation?
a)
x + y = 15
4x + 2y = 44
4x + 2y = 44
b)
4x + 2y = 15
x + y = 44
x + y = 44
c)
x = 2y + 44
4x = y + 15
4x = y + 15
d)
2x - 4y = 44
x - y = 15
x - y = 15
2.
The sum of Mr. Micklow and Ms. Craft's age is 55. The difference is 3.
Solve:
x + y = 55
x - y = 3
Solve:
x + y = 55
x - y = 3
a)
(26, 23)
b)
(26, 29)
c)
(29, 26)
d)
(29, 32)
3.
What is the solution to the system?
a)
(0, 3)
b)
(1, -1)
c)
(-3, 1)
d)
(1, 3)
4.
Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?
a)
x + y = 1550
y = 4x
y = 4x
b)
x + y = 1550
y = x + 4
y = x + 4
c)
y - x = 1550
y = 4x
y = 4x
d)
y = 1550 + x
y = x + 4
y = x + 4
5.
Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have? Which system best represents the situation?
a)
x + y = 1430
20x + 50y = 49
20x + 50y = 49
b)
x + y = 49
10x + 5y = 1430
10x + 5y = 1430
c)
x + y = 49
20x + 50y = 1430
20x + 50y = 1430
d)
x + y = 49
x + y = 1430
x + y = 1430
6.
The senior class at Rivermont High School rented and filled 11 vans and 3 buses with 283 students. The senior class at Washington High School rented and filled 12 vans and 14 buses with 770 students. Which system of equations solves this problem to show how many students were in each van and each bus?
a)
11v + 3b = 283
12v + 14b = 770
b)
v + b = 14
v + b = 16
c)
11v + 12v = 283
3b + 14b = 770
d)
v + b = 30
23v + 17b = 1053
7.
Josh is thinking of two numbers. Their sum is -10 and their difference is -2. Which system of equations represents the situation?
a)
x - y = -10
x + y = -2
x + y = -2
b)
x = -2
y = 5
y = 5
c)
x + y = -2
x - y = -10
x - y = -10
d)
x + y = -10
x - y = -2
x - y = -2
8.
What is the solution to the system?
a)
(0, 3)
b)
(1, -1)
c)
(-3, 1)
d)
(1, 3)
9.
What is the solution?
a)
(6, 3)
b)
(3, 6)
c)
(-6, 3)
d)
No solution
10.
John and Vicki are training for a 5km race. John has already run 20 kilometers and plans to run 10 kilometers each day. Vicki has already run 30 kilometers but plans to run only 5 kilometers per day. The graph below displays each of their training schedules. Which system of equations could be used to determine by which day both John and Vicki will have run the same amount in their training schedule?
a)
John: y = 20x + 10 Vicki: y = 30x + 5
b)
John: y = 10x + 20 Vicki: y = 30x + 5
c)
John: y = -10x + 20 Vicki: y = 5x + 30
d)
John: y = 10x + 20 Vicki: y = 5x + 30
11.
Lisa and Tammy are selling items at the craft show. Which might be a reasonable solution from the graph showing the number of items sold when they both have earned the same amount?
a)
(1, 12)
b)
(3, 19)
c)
(5, 25)
d)
(0, 10)
12.
Two numbers have a sum of 25.
One number is five more than the other number.
Find the numbers. Solve using any method.
a)
The two numbers are 10 and 15.
b)
The two numbers are 10 and 5.
c)
The two numbers are 20 and 5.
d)
The two numbers are 15 and 20.
13.
On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?
a)
10c + 5d = 14.25
5c + 10d = 16.50
5c + 10d = 16.50
b)
10c + 5d = 16.50
5c + 10d = 14.25
5c + 10d = 14.25
c)
c + d = 10
5c + 10d = 16.50
5c + 10d = 16.50
d)
c + d = 5
5c + 10d = 16.50
5c + 10d = 16.50
14.
Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?
a)
y = 9.65 + x
y = 8.40 + x
y = 8.40 + x
b)
y = 9.65x + 43
y = 8.40x + 58
y = 8.40x + 58
c)
y =9.65x
y = 8.40x
y = 8.40x
d)
y = 9.65x - 43
y = 8.40x - 58
y = 8.40x - 58
15.
Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular. One night, the theater sells 578 tickets and collects $3365 in total ticket sales.
Which system best represents the situation?
Which system best represents the situation?
a)
4x + 7y = 578
x + y = 3365
x + y = 3365
b)
4x + 7y = 3365
x + y = 578
x + y = 578
c)
4y + 7x = 578
x + y = 3365
x + y = 3365
d)
4y + 7x = 3365
x + y = 578
x + y = 578
16.
Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.
a)
x + y = 33
y = 2x - 3
y = 2x - 3
b)
x + y = 33
x = 2y - 3
x = 2y - 3
c)
x + y = 33
x = 3 - 2y
x = 3 - 2y
d)
x + y = 3
x = 33 - 2y
x = 33 - 2y
17.
Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Which system of equations represents the situation?
a)
4x + 6y = 3
13.5x - 13y = 6
13.5x - 13y = 6
b)
x + y = 4
x - y = 6
x - y = 6
c)
4x + 6y = 13
3x + 7y = 13.5
3x + 7y = 13.5
d)
4x - 6y = 13
3x - 7y = 13.5
3x - 7y = 13.5
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