Algebra 1 Systems Word Problems

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 system of equations could be used to determine the cost of a cup of coffee and 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

Last season two running backs on the Broncos football team rushed a combined total of 1550 yards.  Player A rushed for 4 times as many yards as player B. How many yards did each player rush for? 

• Player A 1240 yards, Player B 310 yards
• Player A 310 yards, Player B 1240 yards
• Player A 1000 yards, Player B 550 yards
• Player A 550 yards, Player B 1000 yards

David 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, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. How many orders of nachos and how many sodas did he sell?

• 35 nachos, 52 sodas
• 18 nachos, 69 sodas
• 52 nachos, 35 sodas
• 61 nachos, 26 sodas

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 system of equations could you use to determine the number of shirts sold 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

Tags

CCSS.8.EE.C.8C

Erin is 3 years younger than twice Alex's age. The sum of their ages is 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