Systems Word Problems - set up (from Mrs. Math on TPT)

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?

 

A)  T + C = 248          B)  T + C = 248

      T = 26                         T + 26 = C

 

C)  T + C = 124            D)  T = C + 248

      T – C = 26                    T = C + 26

   

E)  None of the above

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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?

 

A)   50t + 30m = 138      B)  50t + 4m = 1500

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

 

C)  50 + 4t = 1500             D)  50t + 30m = 1500

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

 

E)  None of the above

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The Country Buffet restaurant has tables that seat 6 people and booths that can seat 4 people.  The restaurant has 38 seating units for seating a total of 188 people.  Which system of equations could you use to find the number of tables, t, and the number of booths, b, that are at the restaurant?

 

A)    t + b = 38            B)   4t = 38

      6t + 4b = 188               6b = 188

 

C)    t + b = 188          D)     t + b = 38

      6t + 4b = 38                 4t + 6b = 188

 

E) None of the above

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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.

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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

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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.

Evaluate responses using AI:

OFF

A total of 24 students are in Alfred’s class.  The number of girls in the class is 3 more than twice the number of boys.  Which system of equations can be used to find g, the number of girls who are in Alfred’s class, and b, the number of boys?

 

A)  g + b = 24             B)  g + b = 24

      g = 2b + 3                   b = 2g + 3

 

C)  g + b = 24              D)  g + b = 24

      g = 2b – 3                    b = 3 – 2g

 

E) None of the above

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Ted has $6.80 in quarters and dimes.  The number of dimes is 3 times the number of quarters.  Which system of equations can be used to find q, the number of quarters, and d, the number of dimes, that Ted has?

 

A)  q = 3 + d                        B)  d = 3 + q

0.25q + 0.10d = 6.80                  q + d = 6.80

 

C)  q = 3d                             D)  q = 3d

0.25q + 0.10d = 6.80                  q + d = 6.80

 

E)  None of the above  

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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.

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Sarah and James are selling popcorn and cotton candy at the State Fair.  Sarah sold 3 bags of popcorn and 9 sticks of cotton candy for a total of $75.  James sold 8 bags of popcorn and 5 sticks of cotton candy for a total of $67.  Which is cost of the popcorn and stick of cotton candy?

 

 A)  $7 popcorn and $4 cotton candy

B)  $4 popcorn and $7 cotton candy

C)  $6 popcorn and $2 cotton candy

D)  $4 popcorn and $9 cotton candy.

E)  None of the above

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