Paul and Ryan were given some allowances each. If Paul spent $18 each day and Ryan spent $36 each day, Paul would still have $421 left when Ryan spent all his allowance. If Paul spent $36 each day and Ryan spent $18 each day, Paul would still have $43 left when Ryan spent all his allowance.

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

	Case 1		Case 2
	Paul	Ryan	Paul	Ryan
Before	1 u + 421	2 u	2 p + 43	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	421	0	43	0

(a)
Simplify the ratio.
18 : 36 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 43 = 1 u + 421
4 u - 1 u = 421 - 43
3 u = 378

1 u = 378 ÷ 3 = 126

Allowance that Paul received
= 1 u + 421
= 126 + 421
= $547

(b)
Allowance that Ryan received
= 2 u
= 2 x 126
= $252

Answers: (a) $547; (b) $252