Elimination Word Problems

The sum of Mr. Micklow and Ms. Craft's age is 55.  The difference is 3.  Which system of equations represents the situation?

• 2x + 3y = 55
  2x + 5y = 3

• x + y = 55
  x - y = 3

• x + y = 3
  x - y = 55

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

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.  How long does it take her to do a haircut?
3x + 2y = 315
2x + 4y = 450

• 45 minutes

• 90 minutes
  2x + 4y = 315

• 60 minutes
  3x + 4y = 450

• 30 minutes

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. 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

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? 

• c + s = 6
  14.80c + 17s = 91

• c + s = 91
  14.80c + 17s = 6

• c + s = 6
  14.80s + 17c = 91

• c + s = 91
  14.80s+ 17c = 6

Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular. One night, the theater sells 578 tickets and collects $3365 in total ticket sales. 
How many matinee tickets and how many regular tickets were sold?

• 227 regular tickets and 351 matinee tickets

• no solution

• 227 matinee tickets and 351 regular tickets

• 640 matinee and 115 regular tickets

Amanda and Ndiba are selling flower bulbs for a school fundraiser. Customers can buy packages of tulip bulbs (x) and bags of daffodil bulbs (y). Amanda sold 6 packages of tulips and 12 bags of daffodils for a total of $198. Ndiba sold 7 packages of tulips and 6 bags of daffodils for $127. Find the cost of one tulip package and one daffodil bag.

The school that Lisa goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets (x) and 5 student tickets (y) for a total of $102. The school took in $126 on the second day by selling 7 senior citizen tickets and 5 student tickets. What is the price each of one senior citizen ticket and one student ticket?

Castel and Gabriella are selling pies for a school fundraiser. Customers can buy apple and lemon meringue pies. Castel sold 6 apple pies (x) and 4 lemon meringue pies (y) for a total of $80. Gabriella sold 6 apple pies and 5 lemon meringue pies for a total of $94. What is the cost of one apple pie and one lemon meringue pie.

The school that Imani goes to is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 3 senior citizen tickets (x) and 3 child tickets (y) for a total of $69. The school took in $91 on the second day selling 5 senior citizen tickets and 3 child tickets. What is the price of one senior citizen ticket and one child ticket?