Setting Up System of Equations Word Problems

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

Tags

CCSS.HSA.CED.A.3

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

Tags

CCSS.HSA.CED.A.3

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

Tags

CCSS.8.EE.C.8C

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

Tags

CCSS.8.EE.C.8C

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

Tags

CCSS.HSA.CED.A.3

Two college friends rent an apartment. They have to pay the landlord two months rent and a $500 security deposit when they sign the lease. The total amount they pay the landlord is $2800. What is the rent for one month.

• 500 + 2x = 2800

• 500 - 2x = 2800

• 2x - 500 = 2800

• 2800 - 500 = x

Tags

CCSS.HSA.CED.A.3

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 = 9.65x - 43
  y = 8.40x - 58

• y = 9.65x + 43
  y = 8.40x + 58

Tags

CCSS.8.EE.C.8C

Margo is taking a 160-point history test that has a total of 50 questions. Some of the questions are worth 6 points each, and the others are worth 2 points each. Which system of linear equations could be used to find, s, the correct number of six-point questions, and t, the correct number of two-point questions answered correctly?

• s + 6 = 160

  6t + 2s = 50

• 6s = 2t

  s + t = 160

• 6s = 2t

  6s + 2t + 50 = 160

• s + t = 50

  6s + 2t = 160

Tags

CCSS.8.EE.C.8C

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

Tags

CCSS.HSA.CED.A.3

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

Tags

CCSS.8.EE.C.8C