Problem Solving -- Ratios

This is a tricky problem that involves setting up a ratio.

Question: Last year the chess team won 7/9 of its matches. If the team won 16 of its first 32 matches, what was the least number of matches it could have played last year?

(A) 40
(B) 54
(C) 56
(D) 63
(E) 72

Solution:
The key to solving this is setting up the ratio correctly.
Let x = number of additional matches.
You need to add this to both the numerator and denominator, giving
(16+x)/(32+x).
Set this equal to the required ratio, 7/9.
The perform the middle school algebra as follows:
(16+x)/(32+x) = 7/9
9(16+x) = 7(32+x)
144+9x = 224+7x
2x = 80
So, x = 40.
Now, add 40 to the number of matches played (32)
The solution is 72.
Answer choice E.