Set Up Equations Word Problems

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

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

Sally charges $5/hour in her dog walking service, plus a $15 fee to pick up the dogs. Frank charges $10/hour in his dog walking service, but charges no pick-up fee. What set of linear equations below models this information?

• y = 15x + 5
  y = 10x

• y = 5x + 15
  y = 10x

• y = 10x + 5
  y = 15x

• 5x + 15y = 1

  10x = 2

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

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

The sum of Teresa’s and Cathy’s weight is 248 pounds.  Teresa weighs 26 pounds more than Cathy.  If Teresa’s weight is T and Cathy’s weight is C, which of these systems of equations best represents this relationship?

 

T + C = 248          T + C = 248

      T = 26                         T + 26 = C

 

T + C = 124            T = C + 248

      T – C = 26                    T = C + 26

   

None of the above

• A

• B

• C

• D

• E

A television weighs 50 pounds and a microwave weighs 30 pounds.  A TV occupies 4 cubic feet and microwave occupies 3 cubic feet.  A truck is carrying 1500 pounds of cargo that occupies 138 cubic feet of space.  Which system of equations can be used to find the total number of televisions, t, and microwaves, m, that are in the truck?

 

50t + 30m = 138      50t + 4m = 1500

        4t + 3m = 1500             30t + 3m = 138

 

50 + 4t = 1500             50t + 30m = 1500

      30 + 3m = 138                   4t + 3m = 138

 

None of the above

• A

• B

• C

• D

• E

The perimeter of a rectangular wooden deck is 90 sq ft.  The deck’s length is 5 feet less than 4 times its width.  Which system of linear equations can be used to determine the length, L, and width, W, of the wooden deck?

 

A)  2L + 2W = 90          B)  2L + 2W = 90

        L = 5 – 4W                     L = 4W – 5

 

C)  L + W = 90               D)  L + W = 90

      L = 5W – 4                      W = 5 – 4L

 

E)  None of the above.

• A

• B

• C

• D

• E

Mr. Newman 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?

 

A)  8a + 5c = 30             B)   a + c = 8

         a + c = 3                      3a + 5c = 30

 

C)   5a + 3c = 8              D)  5a + 3c = 30

         a + c = 30                     a + c = 8

 

E) None of the above

• A

• B

• C

• D

• E

A group of 28 people attended the fieldtrip.  The number of teachers on the fieldtrip was 20 less than the number of students. 

Write a system of equations that describes the number of teachers, t, and the number of students, s, that went on the fieldtrip.

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