WorksheetsUnit 5.D CW (Part 2): Applications of Systems
Total questions: 15
Worksheet time: 3hrs 30mins
Homer sells tickets to a school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Write a system to represent this situation. Let "a" represent the # of adult tickets and "c" represent the # of children's tickets.
6a + 4c = 104
6a + 4c = 21
6c + 4a = 104
6c + 4a = 21
2p + 3b = 23
2p + 3b = 29.50
2b + 3p = 23
5bp = 23
David is running a concession stand at a soccer game. He sells nachos (N) and sodas (S). 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?
$1.50N + $0.50S = $78.50
N + S = 87
$1.50N + $0.50S = $78.50
$1.50N + $0.50S = 87
N + S = $78.50
$1.50N + $0.50S = 87
N + S = $78.50
N + S = 87
y = 4x
y = x + 4
y = 4x
y = x + 4
y = 2x - 3
x = 2y - 3
x = 3 - 2y
x = 33 - 2y
At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?
t + n = 54
t = 3n + 8
t + n = 54
n = 3t + 8
t + n = 54
t = 3n - 8
t + n = 8
t = 3n + 54
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. If "x" represents the number of shirts and "y" represents the total charge, which equation represents the number of shirts when both companies charge the same amount?
y = 9.65 + x
y = 8.40 + x
y = 9.65x + 43
y = 8.40x + 58
y =9.65x
y = 8.40x
y = 9.65x - 43
y = 8.40x - 58
There are 50 donkeys (d) and chickens (c) on a farm. There are a total of 174 legs. Which system below can be used to figure out how many of each animal the farm has?
d + c = 174
4d + 2c = 50
d + c = 50
4d + 2c = 174
d + c = 50
2d + 4c = 174
d + c = 174
2d + 4c = 50
Flagship Cinemas sells movie tickets that are $4 for matinees (x) and $7 for regular (y). One night, the theater sells 578 tickets and collects $3365 in total ticket sales.
Which system best represents the situation?
4x + 7y = 578
x + y = 3365
4x + 7y = 3365
x + y = 578
4y + 7x = 578
x + y = 3365
4y + 7x = 3365
x + y = 578
.10d + .05n = 80
d + n = 6.60
.10d + .05n = 6.60
.05d + .10n = 6.60
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?
y = 6.80 + .65x
y = 7.30 + .90x
x + y = 6.80
x + y = 7.30
y = 6.80 + .90x
y = 7.30 + .65x
y + .90x = 6.80
y + .65x = 7.30
At a local concert hall, the owner charges $7 per ticket. The owner must pay his band $1200. Every customer receives a brochure that costs the owner $2 for each person.
What system would determine when he breaks even (in other words, when his sales equal his costs).
y = 7x
y = 2x + 1200
y = 2x
y = 7x + 1200
y = 9x + 1200
y = -2x - 1200
y = 7x
John was 20 feet away and was running 5 feet per minute. Alex was 50 feet away and was running 3 feet per minute. Write a system of two equations for this situation.
y = 5x + 20
y = 3x + 50
y = 20x + 5
y = 50x + 3
y = 5x + 50
y = 2x + 20
y = 50x + 5
y = 20x + 3
The Really Awesome Skating Rink was $5 just to get in and costs $3 per hour of skating. The Not As Awesome Skating Rink was $10 just to get in and costs $6 per hour. Write a system of equations for this situation.
y = 3x + 5
y = 6x + 10
y = 5x + 3
y = 10x + 6
y = 3x + 10
y = 6x + 5
y = 5x + 6
y = 10x + 3
The little bunny already ate 20 carrots and then he ate 5 carrots per day. The big bunny already ate 60 carrots and then he ate 25 more carrots per day. Write a system of equations for this situation.
y = 5x + 20
y = 25x + 60
y = 20x + 5
y = 60x + 25
y = 60x + 5
y = 20x + 25
y = 5x + 60
y = 25x + 20
