Ian and Simon were given some allowances each. If Ian spent $16 each day and Simon spent $48 each day, Ian would still have $2603 left when Simon spent all his allowance. If Ian spent $48 each day and Simon spent $16 each day, Ian would still have $43 left when Simon spent all his allowance.

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

	Case 1		Case 2
	Ian	Simon	Ian	Simon
Before	1 u + 2603	3 u	3 p + 43	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2603	0	43	0

(a)
Simplify the ratio.
16 : 48 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 43 = 1 u + 2603
9 u - 1 u = 2603 - 43
8 u = 2560

1 u = 2560 ÷ 8 = 320

Allowance that Ian received
= 1 u + 2603
= 320 + 2603
= $2923

(b)
Allowance that Simon received
= 3 u
= 3 x 320
= $960

Answers: (a) $2923; (b) $960