Ahmad and Liam were given some allowances each. If Ahmad spent $25 each day and Liam spent $50 each day, Ahmad would still have $502 left when Liam spent all his allowance. If Ahmad spent $50 each day and Liam spent $25 each day, Ahmad would still have $52 left when Liam spent all his allowance.

1. How much allowance did Ahmad receive?
2. How much allowance did Liam receive?

	Case 1		Case 2
	Ahmad	Liam	Ahmad	Liam
Before	1 u + 502	2 u	2 p + 52	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	502	0	52	0

(a)
Simplify the ratio.
25 : 50 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 52 = 1 u + 502
4 u - 1 u = 502 - 52
3 u = 450

1 u = 450 ÷ 3 = 150

Allowance that Ahmad received
= 1 u + 502
= 150 + 502
= $652

(b)
Allowance that Liam received
= 2 u
= 2 x 150
= $300

Answers: (a) $652; (b) $300