Paul and Liam were given some allowances each. If Paul spent $11 each day and Liam spent $22 each day, Paul would still have $701 left when Liam spent all his allowance. If Paul spent $22 each day and Liam spent $11 each day, Paul would still have $41 left when Liam spent all his allowance.

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

	Case 1		Case 2
	Paul	Liam	Paul	Liam
Before	1 u + 701	2 u	2 p + 41	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	701	0	41	0

(a)
Simplify the ratio.
11 : 22 = 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 Paul had at first is the same for Case 1 and Case 2.

4 u + 41 = 1 u + 701
4 u - 1 u = 701 - 41
3 u = 660

1 u = 660 ÷ 3 = 220

Allowance that Paul received
= 1 u + 701
= 220 + 701
= $921

(b)
Allowance that Liam received
= 2 u
= 2 x 220
= $440

Answers: (a) $921; (b) $440