Application of Systems

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 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

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

Enterprise charges to rent compact cars for a fixed amount per day plus a fixed amount for each mile driven. Batman rented a car for 6 days, drove it 550 miles and spent $337. Superman rented the same car for 3 days, drove for 350 miles and spent $185. Set up the system. Let "d" represent the fixed charge per day and "m" represent the cost per mile.

• 6d + 550m = 337
  3d + 350m = 185

• 6d + 550m = 185
  3d + 350m = 337

• 6m + 550d = 337
  3m + 350d = 185

• 6m + 550d = 185
  3m + 350d = 337

Adult tickets to a play cost $22. Tickets for children cost $15. Tickets for a group of 11 people cost a total of $228. Which systems of equations below show the number of adult tickets, a, and the number of children tickets, c, that were sold?

• a + c = 228

  22a + 15c = 11

• a + c = 11

  22a + 15c = 228

• a + c = 11

  15a + 22c = 228

• a + c = 228

  15a + 22c = 228

A snack bar sells two sizes of snack packs. A large snack pack, x, is $5, and a small snack pack, y, is $3. In one day, the snack bar sold 60 snack packs for a total of $220. Which system of equations below can be used to show the number of $5 snack packs and the number of $3 snack packs that were sold?

• x + y = 60

  5x + 3y = 220

• x + y = 60

  3x + 5y = 220

• 5x + y = 60

  x + 3y = 220

• x + 3y = 60

  5x + y = 220

Tickets to a school dance cost $12 if you pay before the day of the dance, x, and $15 if you pay the day of the dance, y. The school was able to sell a total of 300 tickets for a total of $4140. Which system of equations below can be used to determine how many of each kind of ticket were sold?

• 12x + y = 4140

  x + 15y = 300

• x + y = 4140

  12x + 15y = 300

• x + y = 300

  12x + 15y = 4140

• x + 15y = 300

  12x + y = 4140

An investor buys 360 shares of two stocks. The price of one stock, x, is $35 per share, while the price of the other stock, y, is $45 per share. The investor pays a total of $15,000 on the two stocks. Which system of equations below could show how many of each stock the investor purchased?

• x + y = 15,000

  45x + 35y = 360

• x + y = 360

  35x + 45y = 15,000

• 35x + y = 360

  x + 45y = 15,000

• x + 45y = 360

  35x + y = 15,000

An investor buys 360 shares of two stocks. The price of one stock, x, is $35 per share, while the price of the other stock, y, is $45 per share. The investor pays a total of $15,000 on the two stocks. Which answer to the system of equations could show how many of each stock the investor purchased?

• 240 shares of stock x, 120 shares of stock y

• 180 shares of stock x, 180 shares of stock y

• 160 shares of stock x, 200 shares of stock y

• 120 shares of stock x, 240 shares of stock y

Your math test has 38 questions on it and is worth 200 points. The test consists of multiple-choice questions, x, wort 4 points each and open-ended questions, y, worth 20 points each. Which system of equations written below shows how you could find the number of each type of question?

• 4x + 20y = 38

  x + y = 200

• x - y = 200

  4x - 20y = 38

• x + y = 38

  4x + 20y = 200

• x - y = 38

  4x - 20y = 200