Setting Up Word Problems Systems

Ben ordered 20 total items consisting of pizza and sodas.  A pizza is $10, a soda is $2, and he spent a total of $72.  Which system models this scenario?

• 10P + 2S = 20
  P + S = 72

• P + S = 20
  2P + 10S = 72

• P + S = 20
  10P + 2S = 72

• y = 10x + 2

  y = 72x + 20

Rachel buys 3 tricycles and 4 bicycles for a total of $72. Joe bought 5 tricycles and 2 bicycles for $50.  Which system models this scenario?

• 3B + 5T = 72
  2T + 4B = 50

• 3T + 4B = 72
  5T + 2B = 50

• 3T + 4B = 50
  5T + 2B = 72

• y = 3x + 4

  y = 5x + 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

Mr. Riley bought 8 tickets to a chili supper and spent a total of $30. He bought a combination of adult tickets for $5 each and child tickets $3 each. Which system of equations below will determine the number of child tickets, c, and the number of adult tickets, a, he bought?

• y = 8x + 30

  y = 5x + 3

• a + c = 8

  3a + 5c = 30

• 5a + 3c = 8

  a + c = 30

• 5a + 3c = 30

  a + c = 8

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

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

• y = 10x + 13

  y = 10x + 13.50

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

Ralph makes $14 per hour plus a $20 bonus.  Melissa makes $12 per hour plus a $15 bonus.  Which system models this scenario?

• y = 14x + 15
  y = 12x + 20

• y = 20x + 14
  y = 15x + 12

• y = 14x + 20
  y = 12x + 15

• 14x + 20y = 1

  12x + 15y = 2

On the first day of a new job; Brandon was sent to a bakery by his boss. Each of the 18 workers gave him an order for either a roll or a muffin. The rolls cost $.40 each, and the muffins cost $.55 each. His boss wrote a company check for $9.15. On the way to the store, Brandon lost the order, but was able to figure out what the order had to be. What was the order? (x = roll, y = muffin)

• 0.4x + 0.55y = 9.15

  x + y = 18

• 0.4x + 0.55y = 18

  x + y = 9.15

• x + 0.55y = 9.15

  0.4x + y = 18  

• 0.4x - 0.55y = 9.15

  x = y + 18

WCHS is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 adult tickets and 1 student ticket for a total of $38. The school took in $52 on the second day by selling 3 adult tickets and 2 student tickets. Find the price of the adult ticket and the price of a student ticket. 

• 3x + y = 38

  3x + 2y = 52

• x + y = 52

  3x + y = 38

• 3x + 2y = 38

  3x + y = 52

• 38x + 52y = 90

  3x + 2y = 1