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WorksheetsSystems of Equations Word Problems
Total questions: 15
Worksheet time: 3hrs 45mins
Name
Class
Date
1.
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?
a)
1s + 3c = 38
2s + 3c = 52
2s + 3c = 52
b)
3s + 1c = 38
3s + 2c = 52
3s + 2c = 52
c)
s + c = 38
s + c = 52
s + c = 52
d)
3s + 3c = 38
1s + 2c = 52
1s + 2c = 52
2.
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
3.
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
4.
Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. How many nickels and dimes did Dennis earn?
a)
40 nickels, 40 dimes
b)
52 nickels, 28 dimes
c)
28 nickels, 52 dimes
d)
30 nickels, 50 dimes
5.
Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?
a)
$5
b)
$10
c)
$15
d)
$20
6.
What is the solution?
a)
No solution
b)
(0, 2)
c)
(0, -4)
d)
(3, -3)
7.
If a system of equations has no solution, what does the graph look like?
a)
intersecting lines
b)
parallel lines
c)
skew lines
d)
intersecting lines
8.
Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Solve the system:
x + y = 21
6x + 4y = 104
x + y = 21
6x + 4y = 104
a)
(10, 11)
b)
(12, 9)
c)
(11, 10)
d)
(9, 12)
9.
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 system of equations represents this situation?
a)
(35, 52)
b)
(18, 69)
c)
( 52, 35)
d)
(61, 26)
10.
Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?
a)
Sugar Cookies $5
Oatmeal Cookies $3
Oatmeal Cookies $3
b)
Sugar Cookies $4
Oatmeal Cookies $8
Oatmeal Cookies $8
c)
Sugar Cookies $2
Oatmeal Cookies $6
Oatmeal Cookies $6
d)
Sugar Cookies $3
Oatmeal Cookies $6
Oatmeal Cookies $6
11.
Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total.
To solve, I graphed:
x + y = 21
6x + 4y = 104
I got an intersection point at (10,11). What does that mean in context of the problem?
a)
There are 10 adults and 11 children.
b)
There are 11 adults and 10 children.
c)
The adults are $10 and the children are $11.
d)
There are 104 adults and 21 children.
12.
A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs. How many of each animal are there?
a)
2 pigs and 8 ducks
b)
10 pigs
c)
8 pigs and 2 ducks
d)
12 pigs and -3 ducks
13.
Solve for x and y
3x + 2y = 16
7x + y = 19
3x + 2y = 16
7x + y = 19
a)
(-2,5)
b)
(-2,-5)
c)
(2,-5)
d)
(2,5)
14.
What is the solution to the system?
8x + 4y = 12
y = -2x + 3
8x + 4y = 12
y = -2x + 3
a)
(0,3)
b)
(3,0)
c)
No solution(parallel lines)
d)
Infinitely many solutions
15.
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
m: # of glasses of milk
b)
t: Cost of each taco
m: Cost of each glass of milk
m: Cost of each glass of milk
c)
t: total cost
m: # of food items
m: # of food items
d)
t: Cost of each glass of milk
m: Cost of each taco
m: Cost of each taco
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