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Given: 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.

Asked: How many tool-kits did Lily buy?

Let toolkit bought by Lily be x and bought by Anthony be y.

Before trade:
Gizmos with Lily = 6x
Gadgets with Lily = 9x
Gizmos with Anthony = 6y
Gadgets with Anthony = 9y

After trade:
Gizmos with Lily = 6x -2/3*6x + = 2x
Gadgets with Lily = 9x + 2/3*9y = 9x +6y
Gizmos with Anthony = 6y + 4x
Gadgets with Anthony = 9y - 6y = 3y

(9x +6y) - 2x = 92
7x + 6y =92

(6y + 4x) - 3y = 50
3y + 4x = 50

x =8
y= 6

Toolkits bought by Lily = x = 8

IMO D

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