Oscar and Ryan were given some allowances each. If Oscar spent $30 each day and Ryan spent $90 each day, Oscar would still have $2927 left when Ryan spent all his allowance. If Oscar spent $90 each day and Ryan spent $30 each day, Oscar would still have $47 left when Ryan spent all his allowance.

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

	Case 1		Case 2
	Oscar	Ryan	Oscar	Ryan
Before	1 u + 2927	3 u	3 p + 47	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2927	0	47	0

(a)
Simplify the ratio.
30 : 90 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 47 = 1 u + 2927
9 u - 1 u = 2927 - 47
8 u = 2880

1 u = 2880 ÷ 8 = 360

Allowance that Oscar received
= 1 u + 2927
= 360 + 2927
= $3287

(b)
Allowance that Ryan received
= 3 u
= 3 x 360
= $1080

Answers: (a) $3287; (b) $1080