Ian and Zane were given some allowances each. If Ian spent $11 each day and Zane spent $22 each day, Ian would still have $1131 left when Zane spent all his allowance. If Ian spent $22 each day and Zane spent $11 each day, Ian would still have $42 left when Zane spent all his allowance.

1. How much allowance did Ian receive?
2. How much allowance did Zane receive?

	Case 1		Case 2
	Ian	Zane	Ian	Zane
Before	1 u + 1131	2 u	2 p + 42	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1131	0	42	0

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

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

1 p = 2 u
2 p = 4 u

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

4 u + 42 = 1 u + 1131
4 u - 1 u = 1131 - 42
3 u = 1089

1 u = 1089 ÷ 3 = 363

Allowance that Ian received
= 1 u + 1131
= 363 + 1131
= $1494

(b)
Allowance that Zane received
= 2 u
= 2 x 363
= $726

Answers: (a) $1494; (b) $726