KEY Review Ch. 9.1,9.2,10.1 and 10.3 -Solving Systems of Linear Equations Word Problems Test
(2.I,5.C
(1) At a family reunion it was decided that as a group adults and children wanted to attend a
play performance. When Mary bought 40 tickets, the bill was $200. If the adult tickets, A,
were $8 and the children tickets, C , were $2, which system best represents this situation?
a)
A + C = 40
A + C = 200
b) 8A + 2C = 40
A + C = 200
c)
2A+ 8C = 200
A + C = 40
d) 8A + 2C = 200
A + C = 40
(2) The sophomore class needs a combined total of 216 medium and large T-shirts for field day.
The number of medium T-shirts needed is three times the number of large T-shirts needed.
Based on this information, would be reasonable for the sophomore class to order 54 large Tshirts and 162 medium T-shirts?
a)No, because the number of medium T-shirts is not 3 times the number of large T-shirts
b) No, because the number of large T-shirts is not 3 times the number of medium T-shirts
c) Yes, because the total number of T-shirts is 216 and the number of medium T-shirts is 3 times
the number of large.
d) Yes, because the total number of T-shirts is 216 and the number of large T-shirts is 3 times
the number of medium.
(3) The graph below shows the distance from Dallas of two cars over a four hour period.
Car A is driving toward Dallas, and Car B is driving away from Dallas.
Based on the graph, when will the two cars be in the same distance from the city?
2
(4) A high school band held a bake sale. The number of muffins, m, sold was four less than
twice the number of cookies, c, sold. The band sold a total of 98 muffins and cookies. Which
of the following is the correct system of equations for this situation?
A. 4 – 2c = m
c + m =98
B. 4 − 2m = c
c + m =98
C. 2c − 4 = m
c + m = 98
D. 2m − 4 = c
m + c = 98
(5) Using question #4, how many muffins were sold at the high school band’s bake sale?
A) 98
B) 49
C) 34
D) 64
(6) There are 20 books stacked on a shelf. The thickness of each book is either 1 inch or 5
inches. The height of the stack of 20 books is 30 inches. Write a system of equations that can
be used determine x, the number of 1-inch-thick books in the stack, and y, the number of 5inch-thick books?
𝑥 + 𝑦 = 20
Equation 1
𝑥 + 5𝑦 = 30
Equation 2
(7) Reserved seat tickets for the football game cost $3.50 each and general admission tickets
cost $2.00 each. After the game is over, the turnstile count shows 1,650 people attended the
game. The total receipts were $4,650. Find the number of each kind of ticket sold.
Equation 1
𝑥 + 𝑦 = 1650
Reserved tickets
Equation 2
900 General Admission tickets
3.50𝑥 + 2𝑦 = 4650
750
(8)Charlie is making a rectangular picture frame. The height of the frame is 6 inches longer than
it width. The perimeter of the frame is 76 inches. Which of these systems of equations below
best describes the dimensions of the picture frame?
a) ℎ + 𝑤 = 6
ℎ + 𝑤 = 76
b )ℎ − 𝑤 = 6
2ℎ + 2𝑤 = 76
c)ℎ + 𝑤 = 6
2ℎ + 2𝑤 = 76
d) ℎ − 𝑤 = 6
ℎ𝑤 = 76