Liam and Pierre were given some allowances each. If Liam spent $23 each day and Pierre spent $46 each day, Liam would still have $901 left when Pierre spent all his allowance. If Liam spent $46 each day and Pierre spent $23 each day, Liam would still have $73 left when Pierre spent all his allowance.

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

	Case 1		Case 2
	Liam	Pierre	Liam	Pierre
Before	1 u + 901	2 u	2 p + 73	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	901	0	73	0

(a)
Simplify the ratio.
23 : 46 = 1 : 2

The allowance that Pierre 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 + 73 = 1 u + 901
4 u - 1 u = 901 - 73
3 u = 828

1 u = 828 ÷ 3 = 276

Allowance that Liam received
= 1 u + 901
= 276 + 901
= $1177

(b)
Allowance that Pierre received
= 2 u
= 2 x 276
= $552

Answers: (a) $1177; (b) $552