George and Michael were given some allowances each. If George spent $15 each day and Michael spent $30 each day, George would still have $999 left when Michael spent all his allowance. If George spent $30 each day and Michael spent $15 each day, George would still have $99 left when Michael spent all his allowance.

1. How much allowance did George receive?
2. How much allowance did Michael receive?

	Case 1		Case 2
	George	Michael	George	Michael
Before	1 u + 999	2 u	2 p + 99	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	999	0	99	0

(a)
Simplify the ratio.
15 : 30 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 99 = 1 u + 999
4 u - 1 u = 999 - 99
3 u = 900

1 u = 900 ÷ 3 = 300

Allowance that George received
= 1 u + 999
= 300 + 999
= $1299

(b)
Allowance that Michael received
= 2 u
= 2 x 300
= $600

Answers: (a) $1299; (b) $600