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Bunuel
A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 2 buckles is how many times that of 5 buckles and 6 buttons?

A. 7/15.
B. 4/9.
C. 6/11.
D. 5/9.
E. 8/15.

Let b = the weight of one button and k = the weight of one buckle. We can create the equation:

2b + 2k = (1/3)(3b + 11k)

6b + 6k = 3b + 11k

3b = 5k

b = 5k/3

In terms of k, 3 buttons and 2 buckles would weigh

3b + 2k = 3(5k/3) + 2k = 5k + 2k = 7k

and 5 buckles and 6 buttons would weigh

6b + 5k = 6(5k/3) + 5k = 10k + 5k = 15k.

Therefore, the weight of 3 buttons and 2 buckles is 7k/(15k) = 7/15 of the weight of 5 buckles and 6 buttons.

Answer: A
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