Peter and Andy were given some allowances each. If Peter spent $12 each day and Andy spent $24 each day, Peter would still have $676 left when Andy spent all his allowance. If Peter spent $24 each day and Andy spent $12 each day, Peter would still have $100 left when Andy spent all his allowance.

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

	Case 1		Case 2
	Peter	Andy	Peter	Andy
Before	1 u + 676	2 u	2 p + 100	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	676	0	100	0

(a)
Simplify the ratio.
12 : 24 = 1 : 2

The allowance that Andy 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 + 100 = 1 u + 676
4 u - 1 u = 676 - 100
3 u = 576

1 u = 576 ÷ 3 = 192

Allowance that Peter received
= 1 u + 676
= 192 + 676
= $868

(b)
Allowance that Andy received
= 2 u
= 2 x 192
= $384

Answers: (a) $868; (b) $384