Charlie and Liam were given some allowances each. If Charlie spent $25 each day and Liam spent $75 each day, Charlie would still have $2457 left when Liam spent all his allowance. If Charlie spent $75 each day and Liam spent $25 each day, Charlie would still have $57 left when Liam spent all his allowance.

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

	Case 1		Case 2
	Charlie	Liam	Charlie	Liam
Before	1 u + 2457	3 u	3 p + 57	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2457	0	57	0

(a)
Simplify the ratio.
25 : 75 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 57 = 1 u + 2457
9 u - 1 u = 2457 - 57
8 u = 2400

1 u = 2400 ÷ 8 = 300

Allowance that Charlie received
= 1 u + 2457
= 300 + 2457
= $2757

(b)
Allowance that Liam received
= 3 u
= 3 x 300
= $900

Answers: (a) $2757; (b) $900