System of Equations Word Problem

John and Vicki are training for a 5km race.  John has already run 20 kilometers and plans to run 10 kilometers each day.  Vicki has already run 30 kilometers but plans to run only 5 kilometers per day. The graph below displays each of their training schedules. Which system of equations could be used to determine by which day both John and Vicki will have run the same amount in their training schedule?

• John: y = 20x + 10    Vicki: y = 30x + 5

• John: y = 10x + 20    Vicki: y = 30x + 5

• John: y = -10x + 20  Vicki: y = 5x + 30

• John: y = 10x + 20  Vicki: y = 5x + 30

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards.  One rushed 4 times as many yards as the other.  Let x and y represent the number of yards each individual player rushed. Which system of equations could be used? 

• x + y = 1550
  y  = 4x

• x + y = 1550
  y = x + 4

• y - x = 1550
  y = 4x

• y = 1550 + x
  y = x + 4

Lisa and Tammy are selling items at the craft show.  Which might be a reasonable solution from the graph showing the number of items sold when they both have earned the same amount?

• (1, 12)

• (3, 19)

• (5, 25)

• (0, 10)

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 equation represents the number of shirts 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

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 school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38
  2s + 3c = 52

• 3s + 1c = 38
  3s + 2c = 52

• s + c = 38
  s + c = 52

• 3s + 3c = 38
  1s + 2c = 52

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 = 6.80+.90x
  y = 7.30 + .65x

• y + .90x = 6.80
  y + .65x = 7.30

At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. If a system of equations is written, which would be the correct representation of the 2 variables?

• t: # of tacos
  m: # of glasses of milk

• t: Cost of each taco
  m: Cost of each glass of milk

• t: total cost
  m: # of food items

• t: Cost of each glass of milk
  m: Cost of each taco

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

• t + n = 54
  t = 3n + 8

• t + n = 54
  n = 3t + 8

• t + n = 54
  t = 3n - 8

• t + n = 8
  t = 3n + 54

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