What total number of apples and bananas?? :s Help!

gmatpup wrote:A certain fruit stand sold apples for $0.70 each and bananas for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase?

A. 10
B. 11
C. 12
D. 13
E. 14

Answer is B

Can someone please explain to me how to do this type of question? I can't seem to grasp the understanding behind it. Thanks so much!!

Let A = no. of apples and B = no. of bananas.
Then 0.7A + 0.5B = 6.30
7A + 5B = 63
5B = 63 - 7A
5B = 7(9 - A)

Now 7(9 - A) is a multiple of 7, so 5B should also be a multiple of 7, which clearly implies that B should be divisible by 7. Now B cannot be 14, because if it so then the bananas would cost more than $6.30, which cannot be the case. So, then b should be 7, and A must then be 4.
5 * 7 = 7 * (9 - 4)
35 = 35 holds true.
Hence, A + B = 4 + 7 = 11

The correct answer is B.