Systems of Equations Set Up Word Problems

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

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

JoAnn likes her job as a baby-sitter, but it pays only $3 per hour. She has been offered a job as a tutor that pays $6 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week. JoAnn wants to to tutor and baby-sit and make at least $66 per week. Formulate an system of inequalities to model how many hours per week she can work at each job.

• b + t < 15
  3b + 6t > 66

• b + t > 15
  3b + 6t < 66

• 3b + 6t > 15
  b + t < 66

• 3b + 6t < 15
  b + t < 66

An electronics store advertised a 19-inch model TV for $349 and a 25-inch model TV for $469.  During one month they sold 44 TVs total and profited an amount of $17,516.  If x represents the number of 19-inch TVs and y represents the number of 25-inch TVs, which system of equation best describes this situation?

 

A)   x + y = 44                        B)    x + y = 44                      

  349x + 469y = 17,516               19x + 25y = 17,516                  

 

C)  349x + 469y = 44            D)   19x + 25y = 44

       x + y = 17,516                       349x + 469y = 17,516

 

E)  None of the above.

• A

• B

• C

• D

• E

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