Peter      [————-3u————–]

Roger      [————-3u————–][——————-4p—————–]

                 [——————————15q————————————-]<——-126——->

Mary       [————3u—————][—————————11q——————————]

                 [—————————————-9p————————————————–]

Mary : 11q + 3u = 9p

Roger:  4p + 3u = 15q

Removing 3u,  we get 11q-4p = 9p – 15q  =>  26q = 13p => p = 2q

Mary has $126 more than Roger, so

9p-15q = 126 => 9(2q)-15q = 126 => 3q = 126 => q = 42

Therefore, p = 2 x 42 = 84

(a)  3u = 9(84) – 11(42) = 756 – 462 = 294  => u = 294/3 = 98

        Each share of bill was $98

(b)  Mary had 9p = 756

        Roger had 15q = 15 x 42 = 630

        Peter had 3u = 294

        Total money they had = 756 + 630 + 294 = 1680    

        Hence sum of Peter’s money as a fraction of their total money = 294/1680 = 7/40

Good lord.  Have mercy on the souls of our poor PSLErs!

This question is ridiculously convoluted.  It’s incredible that you managed to sort it out!

I agree that the question is pretty ridiculous for a 12 year old.  It just shows the prowess of model diagrams being able to sort out the complexity of the problem….and then algebra becomes easier to understand.    Nevertheless, a normal student would totally be turned off after reading the question….lol