WorksheetsSystems of Equations Word Problems 24-25
Total questions: 15
Worksheet time: 15mins
The sum of two numbers is 90. The difference between them is 18.
Write a system of equations that can be used to solve for the numbers.
x - y = 90
x - y = 18
x + y = 90
x + y = 18
x + y = 90
x - y = 18
x - y = 90
x + y = 18
Write a system of equations that can be used to solve for two numbers whose difference is 12 and sum is 86.
x - y = 12
x - y = 86
x + y = 12
x + y = 86
x + y = 12
x - y = 86
x - y = 12
x + y = 86
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?
t: # of tacos
m: # of glasses of milk
t: Cost of each taco
m: Cost of each glass of milk
t: total cost
m: # of food items
t: Cost of each glass of milk
m: Cost of each taco
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?
x + y = 15
4x + 2y = 44
4x + 2y = 15
x + y = 44
x = 2y + 44
4x = y + 15
2x - 4y = 44
x - y = 15
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?
4x + 6y = 3
13.5x - 13y = 6
x + y = 4
x - y = 6
4x + 6y = 13
3x + 7y = 13.5
4x - 6y = 13
3x - 7y = 13.5
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?
x + y = 1430
20x + 50y = 49
x + y = 49
10x + 5y = 1430
x + y = 49
20x + 50y = 1430
x + y = 49
x + y = 1430
A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The rice of each large candle is the same, and the price of each small candle is the same.
Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?
4y = 3x + 64
8y = x + 68
4y = 3x + 64
8y = x + 60
3x + 4y = 64
x + 8y = 68
3x + 4y = 64
x + 8y = 60
There are 15 plates in a kitchen cabinet. The diameter of each plate is either 7 inches or 12 inches. The diameter of all 15 plates combined is 140 inches.
Which system of equations can be used to find the number of 7-inch plates, x, and the number of 12-inch plates, y, that are in the cabinet?
x + y = 140
12x + 7y = 15
7x + 12y = 140
7x + 12y = 15
x + y = 15
7x + 12y = 140
x + y = 15
12x + 7y = 140
Academy sports equipment store is having a sale on bike helmets and water bottles. One bike club purchased 10 helmets and 2 water bottles for $155. Another bike club purchased 12 helmets and 3 water bottles for $189. Which system of equations could be used to determine the cost of a bike helmet and a water bottle?
2h + 10b = 155
12h + 3b = 189
10h + 2b = 189
12h + 3b = 155
10h + 2b = 155
12h + 3b = 189
10h + 3b = 155
12h + 2b = 189
Edwin bought 3 cd's and 7 dvd's for $80. Jessica bought 6 cd's and 3 dvd's for $63.75. Which system of equations could be used to determine how much one cd and one dvd costs?
3x + 7y = 80
6x + 3y = 63.75
3x + 3y = 80
6x + 7y = 63.75
3x + 7y = 63.75
6x + 3y = 80
6x + 7y = 80
3x + 3y = 63.75
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.
x + y = 33
y = 2x - 3
x + y = 33
x = 2y - 3
x + y = 33
x = 3 - 2y
x + y = 3
x = 33 - 2y
Suppose you have 20 coins. If the coins are quarters and nickels only and are worth $2.60, which system of equations would represent this problem?
Let N = # of Nickels and let Q represent the # of Quarters
N + Q = 20
N(5)+Q(25)=2.60
N + Q = 20 N + Q = 2.60
N+Q=20
N(.05)+Q(.25)=2.60
N(.05)+Q(.25)=20 N + Q = 2.60
A drummer and a guitarist each wrote songs for their band. The guitarist wrote 8 fewer than twice the number of songs that the drummer wrote. They wrote a total of 46 songs.
Which system of equations models this situation if the drummer wrote d songs and the guitarist wrote g songs?
g = 2d - 8
g + d = 46
g = 8 - 2d
g = 46 - d
d = 2g - 8
d = 46 - g
d = 8 - 2g
d + g = 46
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
3x + 4y = 30
x = 2y
3x + 4y = 30
y = 2x
3x + 4y = 30
x + y = 2
