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.

Answer 1

Number of trucks = 28

Number of cars = 14

Number of SUVs = 46

Total number of vehicles = 88

Explanation:

Let T = the number of trucks, C = the number of cars, and S = the number of SUVs washed.

We are told :

They washed twice as many cars as trucks.

Hence: T = 2C

They washed a total of 28 trucks and cars and SUVs

Number of trucks = 28

Number of Cars =

T= 2 C

C = T/2

C = 28/2

C = 14

The number of trucks washed was 2 fewer than half the total number of cars and SUVs washed.

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

T = 28

C = 14

Hence:

28 = 1/2(14 + S) - 2

28 = 1/2(14) + 1/2(S) - 2

28 = 7 - 2 +S/2

28 - 7 + 2 = S/2

30 - 7 = S/2

23 = S/2

S = 23 × 2

S = 46

Hence, number of SUVs = 46

Total number of vehicles = 28 + 14 + 46

= 88