Application of Systems of Equations

A student purchased 3 boxes of pencils, x, and 2 boxes of pens, y, for $6. He then purchased 2 boxes of pencils and 4 boxes of pens for $8. Which system of equations below could be used to find the cost of each box of pencils and pens?

• 2x + 2y = 6

  3x + 4y = 8

• 3x + 2y = 6

  2x + 4y = 8

• 3x + 4y = 6

  2x + 2y = 8

• 4x + 2y = 6

  2x + 3y = 8

A student purchased 3 boxes of pencils, x, and 2 boxes of pens, y, for $6. He then purchased 2 boxes of pencils and 4 boxes of pens for $8. What is the cost of each box of pens?

• Each box of pens costs $1.

• Each box of pens costs $1.25.

• Each box of pens costs $1.50.

• Each box of pens costs $1.75.

Two families go to a hockey game. One family purchases two adult tickets and four youth tickets for $33. Another family purchases four adult tickets and five youth tickets for $51.75. What is the cost of an adult ticket and the cost of a youth ticket?

• Adults ticket = $7, Youth tickets = $4.75

• Adult ticket = $6.50, Youth tickets = $5

• Adult ticket = $4.75, Youth ticket = $7

• Adult ticket = $5, Youth ticket = $6.50

On one day Fred's Sports World sold 9 Buffalo Bills jerseys and 3 Miami Dolphins jerseys for a total of $899.40. The next day they sold 12 Bills jerseys and only 2 Dolphins jerseys for a total of $1139.30. How much is the Bills jersey and how much is the Dolphins jersey?

• Bills = $89.95, Dolphins = $29.95

• Bills = $29.95, Dolphins = $89.95

• Bills = $59.95, Dolphins = $39.95

• Bills = $39.95, Dolphins = $59.95

Bob has 60 coins consisting of quarters and dimes. The coins combined values is $13.35. How many of each coin does Bob have?

• 49 quarters, 11 dimes

• 11 quarters, 49 dimes

• 45 quarters, 15 dimes

• 37 quarters, 23 dimes

Jim runs a food cart and during a busy outdoor festival he sold $7343.75 worth of food. He dells hot dogs for $2.95 and steak sandwiches for $9.95. If he sold a total of 985 items that day, how many of each item did he sell?

• 351 hot dogs, 634 steak sandwiches

• 634 hot dogs, 351 steak sandwiches

• 450 hot dogs, 535 steak sandwiches

• 535 hot dogs, 450 steak sandwiches

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

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 answer choice below shows the number of $5 snack packs and the number of $3 snack packs that were sold?

• 10 large snack packs, 50 small snack packs

• 15 large snack packs, 45 small snack packs

• 20 large snack packs, 40 small snack packs

• 25 large snack packs, 35 small snack packs

August bought a total of 8 pounds of peanuts and cashews. Peanuts, p, cost $4 per pound and cashews, c, cost $6 per pound. The total amount August spent on the peanuts and cashews was $42. Which system of equations below could be solved to find how many pounds of peanuts and cashews August bought?

• p + c = 8

  4p + 6c = 42

• 4p + c = 8

  p + 6c = 42

• 4p + c = 42

  p + 6c = 8

• 4p + 6c = 8

  4p + 6c = 42

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