Reggie and Archie were given some allowances each. If Reggie spent $15 each day and Archie spent $45 each day, Reggie would still have $2304 left when Archie spent all his allowance. If Reggie spent $45 each day and Archie spent $15 each day, Reggie would still have $24 left when Archie spent all his allowance.

1. How much allowance did Reggie receive?
2. How much allowance did Archie receive?

	Case 1		Case 2
	Reggie	Archie	Reggie	Archie
Before	1 u + 2304	3 u	3 p + 24	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2304	0	24	0

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

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

1 p = 3 u
3 p = 9 u

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

9 u + 24 = 1 u + 2304
9 u - 1 u = 2304 - 24
8 u = 2280

1 u = 2280 ÷ 8 = 285

Allowance that Reggie received
= 1 u + 2304
= 285 + 2304
= $2589

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

Answers: (a) $2589; (b) $855