Systems of Equations Word Problems

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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?

• 3x + 2y = 315
  2x + 4y = 450

• 3x + 2y = 450
  2x + 4y = 315

• 2x + 2y = 315
  3x + 4y = 450

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

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

Arjun and Liam are planning a road trip. They have two different routes to choose from, each represented by a linear equation. The table shows the distances (in miles) they would travel on each route for different starting points. What is the starting point where both routes have the same distance?

• (-5,-7)

• (-1,5)

• (3,17)

• (8,-59)

The table describes a system of two linear equatios. What is the solution of the system?

• (-2,3)

• (1,3)

• (3, 7)

• (4,9)

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? 

• 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 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?

• S + A = 530
  3S + 4A = 1740

• S + A = 530
  4S + 3A = 1740

• S + A = 1740
  3S + 4A = 530

• S + A = 1740
  4S + 3A = 530

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

A boy has seven more nickels than quarters. The total value of the coins is $4.90. Which system could be used to find out how many nickels and quarters he has?

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