Quote Originally Posted by Adam View Post
I know I'm late on this so I don't expect any points, but I like puzzles so I did it for fun, and since nobody has actually given their method, I thought I would write it out in full so people can see how to solve these things.

Using g for grapefruits, o for oranges and m for lemons (since the 'l' looks too much like a one), we are told -

1) 8g + 7o + 3m = 3o + 6g + 6m
2) g = 2m/3
3) 12o = 3

Straightaway we can work out o - divide both sides of equation 3 by 12 and we get o = 3/12, or 1/4kg. Then if we substitute this value into equation 1, it becomes -

4) 8g + 3m + 7/4 = 6g + 6m + 3/4

Since we also know that 2) g = 2m/3, we can substitute this into equation 4 as well, giving -

5) 8(2m/3) + 3m + 7/4 = 6(2m/3) + 6m + 3/4, which simplifies to
16m/3 + 3m + 7/4 = 12m/3 + 6m + 3/4

Gathering all the m terms on one side of the equation and all the numeric terms on the other gives us -

6) 1 = 5m/3, or 3 = 5m, so m = 3/5kg

And if g = 2m/3 as equation 2 says, then g = 2/3 * 3/5 = 2/5kg.

So that is how we reach the answers of oranges = 1/4kg (250 grams), lemons = 3/5kg (600 grams) and grapefruits = 2/5kg (400 grams).
Nevermind, right.