Last year Charles spent $24,000 total on rare coins, stamps, and books

Last year Charles spent $24,000 total on rare coins, stamps, and books. How much did he spend on rare stamps?

(1) Last year, the amount that Charles spent on stamps and coins combined was five times the amount he spent on books.
(2) Last year, the amount Charles spent on coins was three times the amount spent on stamps and books combined.

My Answer: (C) Both statements together are sufficient

My Approach:

let C,S and B represent amounts spent on rare coins, stamps and books respectively.

Now C+S+B = 24000 (given) -----> equation 1

Statement 1: S+C= 5B

Substituting the value of S+C in equation 1

we get 6B= 24000
B= 4000
S+C = 20000
But we can't find S alone. Therefore, INSUFFICIENT


Statement 2: C= 3(S+B)
Substituting value of C in equation 1 we get
4(S+B) = 24000
S+B = 6000

But we can't find S alone. Therefore, INSUFFICIENT.


BOTH: from Statement 1 and statement 2 together

By substituting the value of B in equation obtained from statement 2

we get, S+4000 = 6000
Thus S=2000, SUFFICIENT

Therefore, (C) BOTH TOGETHER ARE SUFFICIENT.