Ryan and Julian were given some allowances each. If Ryan spent $20 each day and Julian spent $40 each day, Ryan would still have $500 left when Julian spent all his allowance. If Ryan spent $40 each day and Julian spent $20 each day, Ryan would still have $20 left when Julian spent all his allowance.

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

	Case 1		Case 2
	Ryan	Julian	Ryan	Julian
Before	1 u + 500	2 u	2 p + 20	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	500	0	20	0

(a)
Simplify the ratio.
20 : 40 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 20 = 1 u + 500
4 u - 1 u = 500 - 20
3 u = 480

1 u = 480 ÷ 3 = 160

Allowance that Ryan received
= 1 u + 500
= 160 + 500
= $660

(b)
Allowance that Julian received
= 2 u
= 2 x 160
= $320

Answers: (a) $660; (b) $320