Bunuel
An engineering toolkit contains 6 gizmos and 9 gadgets. Anthony and Lily each buy some tool-kits. After both of them complete their purchases, Lily trades two-thirds of her gizmos with Anthony for two-thirds of his gadgets. After the trade, Lily has 92 more gadgets than she has gizmos, and Anthony has 50 more gizmos than he has gadgets. How many tool-kits did Lily buy?
A. 4
B. 5
C. 6
D. 8
E. 10
Are You Up For the Challenge: 700 Level QuestionsWe can let A and L be the number of toolkits Anthony and Lily bought, respectively. Thus, Anthony has 6A gizmos and 9A gadgets, and Lily has 6L gizmos and 9L gadgets. After Lily trades two-thirds of her gizmos (i.e., 4L gizmos) with Anthony for two-thirds of his gadgets (i.e., 6A gadgets), Anthony has 6A + 4L gizmos and 9A - 6A = 3A gadgets, and Lily has 6L - 4L = 2L gizmos and 9L + 6A gadgets.
Since Lily has 92 more gadgets than she has gizmos and Anthony has 50 more gizmos than he has gadgets after the trade, we have:
9L + 6A = 2L + 92
and
6A + 4L = 3A + 50
Simplifying the equations, we have:
7L + 6A = 92
3A + 4L = 50
Multiplying the latter equation by -2, we have -6A - 8L = -100. Adding this equation to 7L + 6A = 92, we have:
-L = -8
L = 8
We see that Lily bought 8 toolkits.
Answer: D