WorksheetsAlgebra: Systems work problems
Total questions: 16
Worksheet time: 1hrs 1mins
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.
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
3.
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. Which system of equations could be used to find the exact number of dimes and nickels?
a)
d + n = 6.60
.10d + .05n = 80
.10d + .05n = 80
b)
d + n = 80
d + n = 6.60
d + n = 6.60
c)
d + n = 80
.10d + .05n = 6.60
.10d + .05n = 6.60
d)
d + n = 80
.05d + .10n = 6.60
.05d + .10n = 6.60
4.
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
5.
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
6.
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
7.
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
8.
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 when both companies cost the same amount?
a)
y = 6.80 + .65x
y=7.30+.90x
y=7.30+.90x
b)
x + y = 6.80
x + y = 7.30
x + y = 7.30
c)
y = 6.80+.90x
y = 7.30 + .65x
y = 7.30 + .65x
d)
y + .90x = 6.80
y + .65x = 7.30
y + .65x = 7.30
9.
Diego scores 11 more points than Travis. Together they score 21 points. How many points did each person score?
a)
Diego: 11, Travis: 10
b)
Diego: 10, Travis: 11
c)
Diego: 5, Travis: 16
d)
Diego: 16, Travis: 5
10.
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
11.
Chase wants to divide $400 between Dylan and Josh. He wants to give Josh 25 more dollars than Dylan how much should each person get?
a)
Dylan $200
Josh $200
Josh $200
b)
Dylan $190
Josh $210
Josh $210
c)
Dylan $195
Josh $205
Josh $205
d)
Dylan $187.50
Josh $212.50
Josh $212.50
12.
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
13.
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
14.
The sum of Mr. Micklow and Ms. Craft's age is 55. The difference is 3. Which system of equations represents the situation?
a)
2x + 3y = 55
2x + 5y = 3
2x + 5y = 3
b)
x + y = 55
x - y = 3
x - y = 3
c)
x + y = 3
x - y = 55
x - y = 55
15.
Two numbers have a sum of 25.
One number is five more than the other number. Find the numbers.
Which system best represents the information?
a)
x + y = 25
x = 5 + y
b)
xy = 25
x = 5 + y
c)
x + y = 25
x = 5y
d)
xy = 25
x = 5y
16.
One number is five more than four times another number. Their sum is 35. Find the two numbers.
Which system best represents the problem?
a)
x = 5 + y
x + y = 35
b)
x = 5 + 4y
x + y = 35
c)
4x = 5 + y
x + y = 35
d)
x = 5 + 4y
xy = 35
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