Simon and Ben were given some allowances each. If Simon spent $18 each day and Ben spent $54 each day, Simon would still have $2761 left when Ben spent all his allowance. If Simon spent $54 each day and Ben spent $18 each day, Simon would still have $25 left when Ben spent all his allowance.

1. How much allowance did Simon receive?
2. How much allowance did Ben receive?

	Case 1		Case 2
	Simon	Ben	Simon	Ben
Before	1 u + 2761	3 u	3 p + 25	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2761	0	25	0

(a)
Simplify the ratio.
18 : 54 = 1 : 3

The allowance that Ben had at first is the same for Case 1 and Case 2.

1 p = 3 u
3 p = 9 u

The allowance that Simon had at first is the same for Case 1 and Case 2.

9 u + 25 = 1 u + 2761
9 u - 1 u = 2761 - 25
8 u = 2736

1 u = 2736 ÷ 8 = 342

Allowance that Simon received
= 1 u + 2761
= 342 + 2761
= $3103

(b)
Allowance that Ben received
= 3 u
= 3 x 342
= $1026

Answers: (a) $3103; (b) $1026