precious stone

[stormgal]

A precious stone was accidentally dropped and broke into 3 stones of equal weight. The value of this type of stone is always proportional to the square of its weight. The 3 broken stones together are worth how much of the value of the original stone?

[jeffedwards]

[spoiler]1/3[/spoiler]

Just pick easy numbers

First stone weighs 9 pounds. We're going to use dollars for the amount to make it easy too
9^2 = $81

Now divide the original weight for each individual stone
9/3=3
3^2= $9

So the original was worth $81
The new stones are each worth $9

Now add the value of the 3 stones (9*3=27...)

So the new total value as a percentage of the original is is 27/81 or 1/3

[backtoschool11]

I agree, picking numbers seems to be the best strategy here.

I picked 6 (lets say ounces) as the original stone's weight. So the original value would be 6^2 or $36.

The three individual pieces would have a weight of 2 ounces each, thus the value of each stone would be 2^2 or $4 each... and the total value of the smaller stones would be 3 * $4 or $12.

Therefore the proportion of the value of the new stones ($12) to the original stone ($36) is 12/36. Which can be simplified to 1/3.

[liferocks]

Let the weight of stone be 3x
so value is 9kx^2 where k is any constant

weight of any of the broken pieces is x
so value of each piece is kx^2

total value of 3 pieces together=3kx^2=(1/3)*(9kx^2)

so The 3 broken stones together are worth 1/3 of the value of the original stone.