Julian and Bryan were given some allowances each. If Julian spent $15 each day and Bryan spent $45 each day, Julian would still have $2343 left when Bryan spent all his allowance. If Julian spent $45 each day and Bryan spent $15 each day, Julian would still have $63 left when Bryan spent all his allowance.

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

	Case 1		Case 2
	Julian	Bryan	Julian	Bryan
Before	1 u + 2343	3 u	3 p + 63	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2343	0	63	0

(a)
Simplify the ratio.
15 : 45 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 63 = 1 u + 2343
9 u - 1 u = 2343 - 63
8 u = 2280

1 u = 2280 ÷ 8 = 285

Allowance that Julian received
= 1 u + 2343
= 285 + 2343
= $2628

(b)
Allowance that Bryan received
= 3 u
= 3 x 285
= $855

Answers: (a) $2628; (b) $855