Homework #3: Writing Systems of Equations from Word Problems

Caitlin won a bag full of money! She has 49 bills in all. She counts $1,430. 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

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

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

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations that represents this situation. Let q represent the number of squash purchased and let z represent the number of zucchini purchased.

• 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

Christian had brochures printed for a new business venture. Christian 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, Christian spent $120 on 3 boxes of black-and-white brochures and 3 boxes of color brochures. Which system represents this situation?

• x+y=134
  x+y=120
• 3x+3y=134
  4x+3y=120
• 4x+3y=134
  3x+3y=120
• 7xy=134
  6xy=120

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. Let h represent the number of haircuts given and d represent the number of hair dyes done. Which system of equations represents the situation?

• 3h + 2d = 315

  2h + 4d = 450

• 3h + 2d = 450

  2h + 4d = 315

• 2h + 4d = 315

  3h + 2d = 450

• 3h + 2d = 315

  2h + 2d = 135

You have a total of 17 coins.  All of your coins are nickels and dimes.  The total value of the coins is $1.35.  Which system of equations represents this situation?

• n+d=17
  .05n+.10d=1.35
• .05n+.10d=17
  n+d=1.35
• .25n+.10d=1.35
  n+d=17

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? 

• y = 9.65 + x
  y = 8.40 + x
• y = 9.65x + 43
  y = 8.40x + 58
• y =9.65x
  y = 8.40x
• y = 9.65x - 43
  y = 8.40x - 58

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

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38

  2s + 3c = 52

• 3s + 1c = 38

  3s + 2c = 52

• s + c = 38

  s + c = 52

• 3s + 3c = 38

  1s + 2c = 52