Setting Up Systems Word Problems

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? 

• x + y = 6
  14.80x + 17y = 91

• x + y = 91
  14.80x + 17y = 6

• x + y = 6
  91y + 17x = 14.80

• x + y = 91
  14.80x+ 17y = 6

Sally charges $5/hour in her dog walking service, plus a $15 fee to pick up the dogs. Frank charges $10/hour in his dog walking service, but charges no pick-up fee. What set of linear equations below models this information?

• y = 15x + 5
  y = 10x

• y = 5x + 15
  y = 10x

• y = 10x + 5
  y = 15x

• 5x + 15y = 1

  10x = 2

There are two taxi companies in Kara's town. The total cost for a ride in a taxi from TaxiTown includes a fixed fee of $4 and then $0.75 per mile. The cost for Quick Ride is given in the table. Which system represents the situation?

• y = .75x + 4

  y = .50x + 5

• y = 4x + .75

  y = 5x + .50

• y = .75x + 4

  y = 5.50x + .50

• .50x + .75y = 5

  .75x + .50y = 4

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount? 

• y = 6.80 + .65x
  y=7.30+.90x

• x + y = 6.80
  x + y = 7.30

• y = .90x + 6.80
  y = .65x + 7.30

• y + .90x = 6.80
  y + .65x = 7.30

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

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. 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

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 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

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

• (2, -2)
• (2, 2)
• (-2, 2)
• (-2, -2)