Writing Systems

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

Tags

CCSS.8.EE.C.8

CCSS.8.F.B.4

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. If x represents the cost of each apple and y represents the cost of each banana, 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? Let S represent the number of student tickets and A represent 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

Saulo is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, Saulo made a total of $78.50 and sold a total of 87 nachos and sodas combined. Let x represent the number of nachos sold and y represent the number of sodas sold. Which system of equations represents this situation?

• 1.5x+0.5y=78.5

  x+y=87

• 1.5x+0.5y=78.5

  1.5x+0.5y=87

• x+y=78.5

  1.5x+0.5y=87

• x+y=78.5

  x+y=87

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Let q represent the cost of each squash and z represent the cost of each zucchini. 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

Tania had 35 coins in pennies and nickels. She had $1.03. Let p represent the number of pennies and n represent the number of nickels. Which system of equations could be used to determine the number of coins she has?

• .01p + .05n = 35

  p + n = 103

• 1p + 5n = 1.03

  p + n = 35

• .01p + .05n = 1.03

  p + n = 35

• .05p + .01n = 1.03

  p + n = 35

You have a total of 17 coins. All of your coins are nickels, n, and dimes, d. 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

There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Let x represent the number of horses and y represent the number of chickens. 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

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills, x, and fifty dollar bills, y. 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

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 time it takes for a haircut. Let D represent the time it takes for a hair dye. 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