Liam and Archie were given some allowances each. If Liam spent $18 each day and Archie spent $36 each day, Liam would still have $943 left when Archie spent all his allowance. If Liam spent $36 each day and Archie spent $18 each day, Liam would still have $79 left when Archie spent all his allowance.

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

	Case 1		Case 2
	Liam	Archie	Liam	Archie
Before	1 u + 943	2 u	2 p + 79	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	943	0	79	0

(a)
Simplify the ratio.
18 : 36 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 79 = 1 u + 943
4 u - 1 u = 943 - 79
3 u = 864

1 u = 864 ÷ 3 = 288

Allowance that Liam received
= 1 u + 943
= 288 + 943
= $1231

(b)
Allowance that Archie received
= 2 u
= 2 x 288
= $576

Answers: (a) $1231; (b) $576