System of Equations Word Problems

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 if x represents the number of horses and y represents the number or chickens?

• 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 if x represents the cost of an apple and y represents the cost of a banana?

• 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

The senior class at Rivermont High School rented and filled 11 vans and 3 buses with 283 students. The senior class at Washington High School rented and filled 12 vans and 14 buses with 770 students. Which system of equations could be used to solve this problem to show how many students were in each van and each bus?

• 11v + 3b = 283

  12v + 14b = 770

• v + b = 14

  v + b = 16

• 11v + 12v = 283

  3b + 14b = 770

• v + b = 30

  23v + 17b = 1053

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, which system could be used to find how many of each type of ticket were sold if s represents the number of student tickets and a represents the number of adult tickets?

• s + a = 530

  3s + 4a = 1740

• s + a = 530

  4s + 3a = 1740

• s + a = 1740

  3s + 4a = 530

• s + a = 1740

  4s + 3a = 530

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?

• x + y = 1550

  y = 4x

• x + y = 1550

  y = x + 4

• y - x = 1550

  y = 4x

• y = 1550 + x

  y = x + 4

Josh is thinking of two numbers.  Their sum is -10 and their difference is -2.  Which system of equations represents the situation?

• x - y = -10
  x + y = -2
• x = -2 
  y = 5
• x + y = -2
  x - y = -10
• x + y = -10
  x - y = -2

Tags

CCSS.HSA.CED.A.3

Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation, if x represents the number of people that ordered chicken and y represents the people that ordered steak?

• x + y = 6

  14.80x + 17y = 91

• x + y = 91

  14.80x + 17y = 6

• x + y = 6

  14.80y + 17x = 91

• x + y = 91

  14.80x+ 17y = 6

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations to represent this situation if q represents the cost of a squash and z represents the cost of a zucchini.

• 5q + 2z = 1.32

  1z = 0.75

• 5q + 2z = 1.32

  3q + 1z = 0.75

• q + z = 1.32

  q + z = 0.75

• 5q + 2z = 0.75

  3q + 1z = 1.32

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 if x represents the number of twenty dollar bills and y represents the number of fifty dollar bills

• x + y = 1430

  20x + 50y = 49

• x + y = 49

  x + y = 1430

• x + y = 49

  20x + 50y = 1430

• x + y = 49

  50x + 20y = 1430

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 a cup of coffee, where c = cost of a cup of coffee and d = the cost of a doughnut.

• 10c + 5d = 14.25

  5c + 10d = 16.50

• 10c + 5d = 16.50

  5c + 10d = 14.25

• c + d = 10

  5c + 10d = 16.50

• c + d = 5

  5c + 10d = 16.50