Peter and Vincent were given some allowances each. If Peter spent $11 each day and Vincent spent $22 each day, Peter would still have $1046 left when Vincent spent all his allowance. If Peter spent $22 each day and Vincent spent $11 each day, Peter would still have $89 left when Vincent spent all his allowance.

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

	Case 1		Case 2
	Peter	Vincent	Peter	Vincent
Before	1 u + 1046	2 u	2 p + 89	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1046	0	89	0

(a)
Simplify the ratio.
11 : 22 = 1 : 2

The allowance that Vincent 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 + 89 = 1 u + 1046
4 u - 1 u = 1046 - 89
3 u = 957

1 u = 957 ÷ 3 = 319

Allowance that Peter received
= 1 u + 1046
= 319 + 1046
= $1365

(b)
Allowance that Vincent received
= 2 u
= 2 x 319
= $638

Answers: (a) $1365; (b) $638