Question

A high school choir had a car wash to raise money. The number of trucks washed was 2 fewer than

half the total number of cars and SUVs washed. They washed twice as many cars as trucks. They
washed a total of 28 trucks and cars and SUVs.
Let T = the number of trucks, C = the number of cars, and S = the number of SUVs washed. Which
ordered triple, (T, C, S) represents the solution to the system below? Verify your answer fully in the
box provided. (5 pts.)
1 2( ) 2
2
28
T CS
C T
TCS
+= +
=
++=
A. (4, 8, 16) C. (8, 16, 4)
B. (4, 8, 12) D. (12, 6, 8)

Answer 1

Answer: C. (8, 16, 4)

Explanation:

Given the following:

Let:

Trucks = T ; Cars = C ; SUVs = S

T =0.5(C + S) - 2 - - - (1)

C = 2T - - - (2)

T + C + S = 28 - - - (3)

T = 0.5(2T + S) - 2

T = T + 0.5S - 2

0 = 0.5S - 2

0.5S = 2

S = 2/0.5

S = 4

From T + C + S = 28

C = 2 T ; S = 4

T + 2T + 4 = 28

3T = 28 - 4

3T = 24

T = 24/3

T = 8

From T + C + S = 28

8 + C + 4 = 28

12 + C = 28

C = 28 - 12

C = 16

Hence, (T, C, S) = (8, 16, 4)