Suppose that you are shopping at a super market and find that the Texas grapefruits have twice the diameter of the Florida ones, but cost seven times as much. Recalling that the volumes of similarly shaped solids vary directly with the cube of a linear dimension such as a diameter, you instantly determine which kind of grapefruit gives you more for your money. Which one does, and why?

these questions are from USA school syllabus. right ?
I don't know exactly
My friend asked this


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Let diameter of florida fruit = d, and its cost = n.
==> Cost per unit volume = cost / volume = n / (d³) ---(1)

Diameter of Texas fruit = 2d, and its cost = 7n.
==>Cost per unit volume = cost / volume = (7n) / (2d)³ = (7n) / (8d³) --(2)

Comparing cost per unit volume (1) and (2),
n / (d³) : (7n) / (8d³) = 1 : (7/8)  
Hence Texas grapefruit give you more for money as you have to pay less per unit volume.
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