Apples varied directly

Question

Apple's varied directly as bananas squared and inversely as watermelons. When there were 60 apples, there were 4 bananas and 8 watermelons. How many apples were there when there were 6 bananas and only 3 watermelons?

Answer 1

A - Apples, B - Bananas, W - watermelons. Given that the apples are related to bananas squared A ~ B² and inversely with watermelons A ~ 1/W. We have that then A₂/A₁ = (B₂/B₁)² + W₁/W₂. (This assumes equal "weight" of bananas influence and watermelons, but without that, the problem is underspecified). From this equation we can get that A₂ = 60*((6/4)²+ (8/3)) = 60*(9/4 + 8/3) = 15*9 + 20*8 = 295. This intuitively makes sense since there is less watermelons (increasing A) and more bananas (increasing A).