Multi Variable

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are $20 bills and $50 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

The admission fee at a small fair is $2 for children and $4 for adults. On a certain day $5,050 is collected. Write an equation to model this situation. No spaces. Use x and y.

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If e=Erin's age and a=Alex's age, choose the system that matches the situation.

• e + a = 33
  a = 2e - 3

• a + e = 33
  e = 2a - 3

• a + e = 33
  a = 3 - 2e

• e + a = 33
  e = 33 - 2e

Andrea needed to purchase clothes for the fall.  Her favorite store extended the Labor Day sale.  The cost of 4 pairs of pants, 3 shirts, and 2 sweater is $126.  The cost of 1 pair of pants and 4 shirts is $55.  The cost of 4 shirts and 4 sweaters is $112.  If x represents pants, y represents shirts, and z represents sweaters, which system of equations can be used can be used to determine the sale price of the pants, shirts, and sweaters?

Gisel wanted to buy some music with some of the birthday money she recently received.  The cost of 3 audio cassettes, 2 audio cd, and 4 vinyl records was $175.  The cost of 4 cd’s and 1 vinyl record is $97.  The cost of 4 cassettes and 2 vinyl records is $102.  If x represents cassettes, y represents cd’s, and z represents vinyl records, which system of equations can be used can be used to determine the sale price of the cassette, cd’s, and vinyl records?

You are selling tickets at a high school football game. Student tickets cost $3 and general admission tickets cost $4. You sell 1075 tickets and collect $3875.

Which system of equations represents this situation?

• 3x+4y=3875

  x+y=1075

• 3x+4y=1075

  x+y=3875

• 3x+y=3875

  4x+y=1075

• 4x+y=3875

  3x+y=1075

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.

Which system best represents the situation?

• 4x + 7y = 578

  x + y = 3365

• 4x + 7y = 3365

  x + y = 578

• 4y + 7x = 578

  x + y = 3365

• 4y + 7x = 3365

  x + y = 578

A company opened two new branches. Branch M began with 26 clients and gains 3 more per week. Branch Q began with 18 clients and gains 5 more per week. Write a system of equations to compare the number of clients (c) each branch has after (w) weeks.

• 26c + 3w

  18c + 5w

• c = 3w + 26

  c = 5w + 18

• c = 26c + 3w

  c = 18c + 5w

• w = 26 + 3c

  w = 18 + 5c

David is 4 years older than his brother Gabriel. Together, their age is equal to 22. Which system of equation can be used to find David's age, d, and Gabriel's age, g?

Traveling downstream, a certain boat went 19 miles in 6 hours. The return trip took 8 hours. Which system of equations can be used to find speed of the current, c, and speed of the boat, b, in still water?

• 6(b + c) = 19

  8(b - c) = 19

• 6(b - c) = 19

  8(b + c) = 19

• b - c = 19

  8b + 6c = 19

• b + c = 19

  8b - 6c = 19