Systems of Equations Set Up Word Problems

JoAnn likes her job as a baby-sitter, but it pays only $3 per hour. She has been offered a job as a tutor that pays $6 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week. How many hours can JoAnn tutor and baby-sit and still make at least $66 per week? How much does she make?

• b + t < 15
  3b + 6t > 66

• b + t > 15
  3b + 6t < 66

• 3b + 6t > 15
  b + t < 66

• 3b + 6t < 15
  b + t < 66

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. To solve, I graphed: x + y = 21 6x + 4y = 104 I got an intersection point at (10,11). What does that mean in context of the problem?

• There are 10 adults and 11 children.

• There are 11 adults and 10 children.

• The adults are $10 and the children are $11.

• There are 104 adults and 21 children.

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

• 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

John was 20 feet away and was running 5 feet per minute. Alex was 50 feet away and was 3 feet per minute. Write a system of two equations for this situation?

• y = 5x + 20

  y = 3x + 50

• y = 20x + 5

  y = 50x + 3

• y = 5x + 50

  y = 2x + 20

• y = 50x + 5

  y = 20x + 3

A water tank (t) holds 256 gallons but is leaking at a rate of 3 gallons (g) per week. A second water tank (t) holds 384 gallons but is leaking at a rate of 5 gallons (g) per week. After how many weeks will the amount in the two tanks be the same?

• 3g + 5g = 640

  W = 256 + 384

• W = 256 - 3g

  W = 384 - 5g

• W = 256 + 3g

  W = 384 + 5g

Answer explanation

Remember that decreasing will be subtraction.

Rachel buys 3 tricycles and 4 bicycles for a total of $72. Joe bought 5 tricycles and 2 bicycles for $50.  Which system models this scenario?

• 3B + 5T = 72
  2T + 4B = 50

• 3T + 4B = 72
  5T + 2B = 50

• 3T + 4B = 50
  5T + 2B = 72

• y = 3x + 4

  y = 5x + 2

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

• y = 10x + 13

  y = 10x + 13.50

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
  91y + 17x = 14.80

• x + y = 91
  14.80x+ 17y = 6

Ralph makes $14 per hour plus a $20 bonus.  Melissa makes $12 per hour plus a $15 bonus.  Which system models this scenario?

• y = 14x + 15
  y = 12x + 20

• y = 20x + 14
  y = 15x + 12

• y = 14x + 20
  y = 12x + 15

• 14x + 20y = 1

  12x + 15y = 2

Ben ordered 20 total items consisting of pizza and sodas.  A pizza is $10, a soda is $2, and he spent a total of $72.  Which system models this scenario?

• 10P + 2S = 20
  P + S = 72

• P + S = 20
  2P + 10S = 72

• P + S = 20
  10P + 2S = 72

• y = 10x + 2

  y = 72x + 20