Asher and Paul were given some allowances each. If Asher spent $11 each day and Paul spent $33 each day, Asher would still have $1806 left when Paul spent all his allowance. If Asher spent $33 each day and Paul spent $11 each day, Asher would still have $46 left when Paul spent all his allowance.

1. How much allowance did Asher receive?
2. How much allowance did Paul receive?

	Case 1		Case 2
	Asher	Paul	Asher	Paul
Before	1 u + 1806	3 u	3 p + 46	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1806	0	46	0

(a)
Simplify the ratio.
11 : 33 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 46 = 1 u + 1806
9 u - 1 u = 1806 - 46
8 u = 1760

1 u = 1760 ÷ 8 = 220

Allowance that Asher received
= 1 u + 1806
= 220 + 1806
= $2026

(b)
Allowance that Paul received
= 3 u
= 3 x 220
= $660

Answers: (a) $2026; (b) $660