cronkey7 wrote:
A total of n trucks and cars are parked in a lot. If the number of cars is 1/4 the number of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of n, are parked in the lot?
A. 1/6 n
B. 5/12 n
C. 1/2 n
D. 8/15 n
E. 11/12 n
I decided to use 100 for the total of trucks + cars. So n = 100.
Number of cars = 1/4 # of trucks, then there are 25 cars and 75 trucks
2/3 of the trucks are pickups, so 2/3 of 75 is 50.
Therefore, the number of pickups (50) in terms of n would be (1/2)n, which equals 100 * 1/2 = 50, the number of pickups. = C
However, this is not the correct answer- the correct answer is D, 8/15. Can someone explain???
C = Cars, T = Trucks, and P = Pickups.
\(C + T = n\)
\(C = \frac{1}{4} T\)
\(\frac{2}{3}T = P\)
We'd like to write everything in terms of Pickups, since that's what the question is asking us about. Thus,
\(T = \frac{3}{2}P\),
\(C = \frac{1}{4}T = \frac{1}{4} * \frac{3}{2} P = \frac{3}{8}P\)
Therefore,
\(n = C + T = \frac{3}{8} P + \frac{3}{2} P = \frac{30}{16}P = \frac{15}{8}P.\)
Solving for P, we see that \(P = \frac{8}{15} n.\)
Answer: D