>Yeah, it's hard to explain when I cant draw the boxes very well. Let me try again.
>
>

>An example:
>
>You can use more than one "work" column to get to the result.
>
>. Known   Work    Work    Result
>---------------------------------
>|  16   |  48   |  24   |  12   |
>|--------------------------------
>|  28   |  84   |  42   |   X   |
>---------------------------------
>
>First row logic:
>
>(((16 * 3) / 2) / 2) = 12 (there are other solutions other than * 3 / 2 / 2)
>((48 / 2) / 2) = 12
>24 / 2 = 12
>
>
>Use same logic on second row:
>
>(((28 * 3) / 2) / 2 = X
>((84 / 2) / 2) = X
>42 / 2 = X
>21 = X
>
>
>The one I can't solve without fractions or decimals.
>
>This is how the table looks (could be more than one "work" column though).
>
>. Known   Work    Result
>-------------------------
>|  50   |       |  18   |
>|------------------------
>|  60   |       |   X   |
>-------------------------
>

OK, I think I see what you're doing. In your first (solved) example, each column is the ratio of 4/7 (top/bottom). This holds true for both the intermediate, "work" columns. As I see it you can have as many work columns as you want, and their ratios top/bottom should all be 4/7. So, in the first example X = 12 * ( 7 / 4 ) = 21.

In the second example, the ratio top/bottom is always 5/6. No matter how many work columns you have, they should all maintain this ratio. The final column should maintain it as well, so the result is X = 18 * ( 6 / 5 ) = 108 / 5 = 21.6.

If the answer is supposed to be integer, the simplest explanation I can think of is there is a misprint in the question. For example, if the first "known" column was 40/60 instead of 50/60 then X would be 27. Or if the known "result" value was 180 instead of 18, then X would be 216.

Or maybe this is a *purposeful* "mistake". Getting kids scratching their heads over this probably reinforces the learning. Perhaps kids who point out the problem get extra credit?