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Unit 5.D CW (Part 2): Applications of Systems

Total questions: 15

Worksheet time: 3hrs 30mins

Name
Class
Date
1.

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.

a)
a + c = 21
6a + 4c = 104
b)
a + c = 104
6a + 4c = 21
c)
a + c = 21
6c + 4a = 104
d)
a + c = 104
6c + 4a = 21
2.
Michelangelo decided to order Pizza Hut last night. He purchased 3 pizzas and 2 orders of breadsticks for a total of $29.50. Donatello ordered 2 pizzas and 3 orders of breadsticks last Sunday for a total of $23. Set up a system. Let "p" represent the price per pizza and "b" represent the price of an order of breaksticks.
a)
3p + 2b = 29.50
2p + 3b = 23
b)
3p + 2b = 23
2p + 3b = 29.50
c)
3b + 2p = 29.50
2b + 3p = 23
d)
5bp = 29.50
5bp = 23
3.

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?

a)

$1.50N + $0.50S = $78.50

N + S = 87

b)

$1.50N + $0.50S = $78.50

$1.50N + $0.50S = 87

c)

N + S = $78.50

$1.50N + $0.50S = 87

d)

N + S = $78.50

N + S = 87

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
b)
x + y = 1550
y = x + 4
c)
y - x = 1550
y = 4x
d)
y = 1550 + x
y = x + 4
5.
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
b)
x + y = 33
x = 2y - 3
c)
x + y = 33
x = 3 - 2y
d)
x + y = 3
x = 33 - 2y
6.

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?

a)

t + n = 54

t = 3n + 8

b)

t + n = 54

n = 3t + 8

c)

t + n = 54

t = 3n - 8

d)

t + n = 8

t = 3n + 54

7.

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?

a)

y = 9.65 + x

y = 8.40 + x

b)

y = 9.65x + 43

y = 8.40x + 58

c)

y =9.65x

y = 8.40x

d)

y = 9.65x - 43

y = 8.40x - 58

8.

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?

a)

d + c = 174

4d + 2c = 50

b)

d + c = 50

4d + 2c = 174

c)

d + c = 50

2d + 4c = 174

d)

d + c = 174

2d + 4c = 50

9.

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?

a)

4x + 7y = 578

x + y = 3365

b)

4x + 7y = 3365

x + y = 578

c)

4y + 7x = 578

x + y = 3365

d)

4y + 7x = 3365

x + y = 578

10.
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
b)
d + n = 80
d + n = 6.60
c)
d + n = 80
.10d + .05n = 6.60
d)
d + n = 80
.05d + .10n = 6.60
11.

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

12.

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).

a)

y = 7x

y = 2x + 1200

b)

y = 2x

y = 7x + 1200

c)

y = 9x + 1200

d)

y = -2x - 1200

y = 7x

13.

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.

a)

y = 5x + 20

y = 3x + 50

b)

y = 20x + 5

y = 50x + 3

c)

y = 5x + 50

y = 2x + 20

d)

y = 50x + 5

y = 20x + 3

14.

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.

a)

y = 3x + 5

y = 6x + 10

b)

y = 5x + 3

y = 10x + 6

c)

y = 3x + 10

y = 6x + 5

d)

y = 5x + 6

y = 10x + 3

15.

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.

a)

y = 5x + 20

y = 25x + 60

b)

y = 20x + 5

y = 60x + 25

c)

y = 60x + 5

y = 20x + 25

d)

y = 5x + 60

y = 25x + 20