Question

A sum of money is to be divided between Alyah, Byron and Cecil. Alyah receives $1 plus one-third of what is left. Byron then receives $6 plus one-third of what remains. Cecil receives the rest, which amounts to $40. How much did Byron receive? (A) $26 (B) $28 (C) $30 (D) $32 (E) $34​

Answer 1

(A) $26

Explanation:

You want to know the amount Byron received from the distribution to Alyah, Byron, and Cecil, given Cecil received $40.

Setup

Let x represent the amount being distributed, and a, b, c represent the amounts received by Alyah, Byron, and Cecil, respectively.

The given relations tell us ...

a = 1 + 1/3(x -1)

b = 6 + 1/3(x -a -6)

c = x -a -b = 40

Solution

Substituting for b gives us ...

40 = x - a - (6 +1/3(x -a -6)) = x -a -6 -1/3x +1/3a +2 = 2/3x -2/3a -4

44 = 2/3(x -a) . . . . . . . add 4, factor out 2/3

66 = x -a . . . . . . . . . multiply by 3/2

Substituting for a gives us ...

66 = x -(1 +1/3(x -1)) = x -1 -1/3x +1/3 = 2/3x -2/3 = 2/3(x -1)

99 = x -1 . . . . . . . multiply by 3/2

100 = x . . . . . . add 1

Distribution

Then ...

a = 1 + 1/3(100 -1) = 1 + 99/3 = 34

b = 6 + 1/3(100 -34 -6) = 6 + 1/3(60) = 26

Byron received $26.

__

Additional comment

Based on results, the "what is left" is the amount after the $1 or $6 distributions are made.

Alyah: $34, Byron: $26, Cecil: $40, for a total of $100.

<95141404393>