Question

A sum of money is to be divided among Allan, Bill and Carol. Allan receives $1 plus 1/3 of what is left. Bill then receives $6 plus 1/3 of what is remains. Carol receives the rest, which amounts to $40. How much did Bill receive?

Answer 1

a- $26
b-28
c-30
d-32
e-34

Answer 2

This is a really tricky problem. The Allan character dosen't matter because we don't know how much we started with. After Bill is blessed, Carol gets $40. We need to work backwards from Carol's amount. The problem is modeled by simple Algebra. In words, Bill gets $6 plus one third of the remaining money and after that, there is $40 left.
Let A be the amount that is left for Bill to dive into. A - $6 - 1/3(A-$6) = $40
add $6 to each side and multiply by 3
3A - A + $6 = $138
A = $66
Bill's part is 1/3(A - $6) + $6, which is equal to $26