George and Vincent were given some allowances each. If George spent $22 each day and Vincent spent $66 each day, George would still have $2740 left when Vincent spent all his allowance. If George spent $66 each day and Vincent spent $22 each day, George would still have $100 left when Vincent spent all his allowance.

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

	Case 1		Case 2
	George	Vincent	George	Vincent
Before	1 u + 2740	3 u	3 p + 100	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2740	0	100	0

(a)
Simplify the ratio.
22 : 66 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 100 = 1 u + 2740
9 u - 1 u = 2740 - 100
8 u = 2640

1 u = 2640 ÷ 8 = 330

Allowance that George received
= 1 u + 2740
= 330 + 2740
= $3070

(b)
Allowance that Vincent received
= 3 u
= 3 x 330
= $990

Answers: (a) $3070; (b) $990