Liam and Warren were given some allowances each. If Liam spent $27 each day and Warren spent $81 each day, Liam would still have $1966 left when Warren spent all his allowance. If Liam spent $81 each day and Warren spent $27 each day, Liam would still have $22 left when Warren spent all his allowance.

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

	Case 1		Case 2
	Liam	Warren	Liam	Warren
Before	1 u + 1966	3 u	3 p + 22	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1966	0	22	0

(a)
Simplify the ratio.
27 : 81 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 22 = 1 u + 1966
9 u - 1 u = 1966 - 22
8 u = 1944

1 u = 1944 ÷ 8 = 243

Allowance that Liam received
= 1 u + 1966
= 243 + 1966
= $2209

(b)
Allowance that Warren received
= 3 u
= 3 x 243
= $729

Answers: (a) $2209; (b) $729