every car at a certain dealership is either a convertible, a sedan, or both. if 1/5 of the convertibles are?

Question

every car at a certain dealership is either a convertible, a sedan, or both. if 1/5 of the convertibles are also sedans and 1/3 of the sedans are also convertibles, which of the following could be the talta number of cars at the dealership....

ok so the answer is 28
but how do you solve this to get 28?

oh sorry ...what i meant by "talta" is "total"...but i`m sure you all knew that =D

Answer 1

Let's assume that...
the number of convertibles that are not sedans is "C"
the number of sedans that are not convertibles is "S"
the number of vehicles that are both is "B"

We know that:
the total number of sedans is S + B.
the total number of convertibles is C + B.

1/3 of the sedans are also convertibles, so:
B / (S + B) = 1/3
B = 1/3*(S + B)
B = 1/3*S + 1/3*B
2/3*B = 1/3*S
2*B = S

1/5 of the convertibles are also sedans, so:
B / (C + B) = 1/5
B = 1/5*(C + B)
B = 1/5*C + 1/5*B
4/5*B = 1/5*C
4*B = C

If B = 1, then S = 2 and C = 4, so B + S + C = 7.
If B = 2, then S = 4 and C = 8, so B + S + C = 14.
If B = 3, then S = 6 and C = 12, so B + S + C = 21.

See a pattern emerging? B can be any integer, and S and C are related to B by the equations I derived. The total number of cars in the lot (B+S+C) always equals a multiple of seven for every integer value of B, so any answer that is a multiple of seven is a possibility. I'm assuming 28 was the only multiple of seven among the answer choices.

Answer 2

Let C = #true convertibles,
S = #true sedans
B = #cars that are both

C = (4/5)(C+B) or 0.2C = 0.8B or C=4B
S = (2/3)(S+B) or (1/3)S = (2/3)B or S=2B

Total #cars = C +S +B
= 4B + 2B + B
= 7B, or a multiple of 7

I assume 28 is the only answer shown that is a multiple of 7.