Question

A, B, C are stamp collectors. A has 18 stamps more than B. Ratio of the number of stamps of B to that of C is 7:5. the ratio of the sum of B's and C's stamps to that of A's stamps is 6:5. Find how many stamps does C have

Answer 1

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Answer:

C has 30 stamps

Step-by-step explanation:

1. A has 18 stamps more than B: A = 18 + B
2. Ratio of stamps of B and C: B/C = 7/5
3. Ratio of Sum of B and C to A: (B+C)/A=6/5

In the equation (B+C)/A=6/5 , substitute the value of A as 18+B .... from (1)

So, it will be (B+C)/18+B=6/5.

Now, cross multiply it.

5(B+C)=6(18+B)

5B+5C=108+6B

-108+5C=6B-5B

-108+5C=B

So, the value of B is -108+5C.

Now, in the equation B/C=7/5, we will substitute the value of B as -108+5C

So, the equation formed will be:

(-108+5C)/C=7/5

5(-108+5C)=7(C)

-540+25C=7C

25C-7C=540

18C=540

C=540/18

C=30

Therefore, C has collected 30 stamps.