Peter and Rael were given some allowances each. If Peter spent $24 each day and Rael spent $48 each day, Peter would still have $567 left when Rael spent all his allowance. If Peter spent $48 each day and Rael spent $24 each day, Peter would still have $63 left when Rael spent all his allowance.

1. How much allowance did Peter receive?
2. How much allowance did Rael receive?

	Case 1		Case 2
	Peter	Rael	Peter	Rael
Before	1 u + 567	2 u	2 p + 63	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	567	0	63	0

(a)
Simplify the ratio.
24 : 48 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 63 = 1 u + 567
4 u - 1 u = 567 - 63
3 u = 504

1 u = 504 ÷ 3 = 168

Allowance that Peter received
= 1 u + 567
= 168 + 567
= $735

(b)
Allowance that Rael received
= 2 u
= 2 x 168
= $336

Answers: (a) $735; (b) $336