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Application of Systems of Linear Equations

Total questions: 21

Worksheet time: 1hrs 15mins

Name
Class
Date
1.
The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, how many of each type of ticket were sold?
a)
S + A = 530
3S + 4A = 1740
b)
S + A = 530
4S + 3A = 1740
c)
S + A = 1740
3S + 4A = 530
d)
S + A = 1740
4S + 3A = 530
2.

Pilar had brochures printed for a new business venture. Pilar originally ordered 4 boxes of black-and-white brochures and 3 boxes of color brochures, which cost a total of $134. After those ran out, Pilar spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?

a)

x+y=134

x+y=120

b)

3x+3y=134

4x+3y=120

c)

4x+3y=134

3x+3y=120

d)

7xy=134

6xy=120

3.

Saulo 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, Saulo made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

a)

1.5x+0.5y=78.5

x+y=87

b)

1.5x+0.5y=78.5

1.5x+0.5y=87

c)

x+y=78.5

1.5x+0.5y=87

d)

x+y=78.5

x+y=87

4.
At a holiday ski resort, skis cost $16 to rent and snowboards cost $19. If 28 people rented on a certain day and the resort brought in $478, which system could be used to determine the number of skis (s) and snowboards (b) rented?
a)
s+b=478
19s+16b=28
b)
s + b = 28
16s+19b=478
c)
s+b=478
16s+19b=28
d)
s+b=28
19s+16b=478
5.

A store sells oatmeal cookies for $2 and chocolate cookies for $3. On a busy day, the store sold 8 more oatmeal cookies than chocolate cookies and made $156. Which system of equations can be used to determine how many of each kind of cookies were sold.

a)

2x + 3y = 156

x = y + 8

b)

2x + 3y = 156

y = x + 8

c)

2x + 3y = 156

x + y = 156

d)

2x + 3y = 156

x + y = 8

6.
Your family goes to a southern style restaurant for dinner. There are 6 total people in your family. Some order chicken for $14 and the rest order steak for $17. The total bill is $99. Write a system that could represent this situation.
a)
c + s = 6
14c + 17s = 99
b)
c + s = 99
14c + 17s = 6
c)
c + s = 6
17c + 14s = 99
d)
c + s = 99
17c + 14s = 6
7.

Tania had 35 coins in pennies and nickels. She had $1.03. Which system of equations could be used to determine the number of coins she has?

a)

.01p + .05n = 35

p + n = 103

b)

1p + 5n = 1.03

p + n = 35

c)

.01p + .05n = 1.03

p + n = 35

d)

.05p + .01n = 1.03

p + n = 35

8.

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. Choose the system that can be used to determine Erin and Alex's age.

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
9.
Caitlin won a bag full of money! She has 49 bills in all. She counts $1,430. There are $20 dollar bills and $50 dollar bills. How many of each bill does Caitlin have?
WRITE a system where T= # of $20 and F = # of $50.
a)
T + F = 1430
20T + 50F = 49
b)
T+ F = 49
10T + 5F = 1430 
c)
T + F = 49
20T + 50F  = 1430
d)
T + F = 49
T + F = 1430
10.

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
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
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 when both companies cost 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.

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

b)

x + y = 4

x - y = 6

c)

4x + 6y = 13

3x + 7y = 13.5

d)

4x - 6y = 13

3x - 7y = 13.5

13.

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $68 for 1 large candle and 8 small candles.

Which system of equations can be used to find the price in dollars of each large candle and each small candle?

a)

4y = 3x + 64

8y = x + 68

b)

4y = 3x + 64

8y = x + 60

c)

3x + 4y = 64

x + 8y = 68

d)

3x + 4y = 64

x + 8y = 60

14.

There are 50 donkeys and chickens 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
15.
Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?
a)
3x + 2y = 315
2x + 4y = 450
b)
3x + 2y = 450
2x + 4y = 315
c)
2x + 2y = 315
3x + 4y = 450
16.

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.

a)

5q + 2z = 1.32

1z = 0.75

b)

5q + 2z = 1.32

3q + 1z = 0.75

c)

q + z = 1.32

q + z = 0.75

d)

5q + 2z = 0.75

3q + 1z = 1.32

17.

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. Which system of equations could be used to determine the number of yards each running back rushed? 

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
18.
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
b)
x = -2 
y = 5
c)
x + y = -2
x - y = -10
d)
x + y = -10
x - y = -2
19.

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
b)
10c + 5d = 16.50
5c + 10d = 14.25
c)
c + d = 10
5c + 10d = 16.50
d)
c + d = 5
5c + 10d = 16.50
20.

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
21.

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