Reggie and Michael were given some allowances each. If Reggie spent $10 each day and Michael spent $20 each day, Reggie would still have $1083 left when Michael spent all his allowance. If Reggie spent $20 each day and Michael spent $10 each day, Reggie would still have $63 left when Michael spent all his allowance.

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

	Case 1		Case 2
	Reggie	Michael	Reggie	Michael
Before	1 u + 1083	2 u	2 p + 63	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1083	0	63	0

(a)
Simplify the ratio.
10 : 20 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 63 = 1 u + 1083
4 u - 1 u = 1083 - 63
3 u = 1020

1 u = 1020 ÷ 3 = 340

Allowance that Reggie received
= 1 u + 1083
= 340 + 1083
= $1423

(b)
Allowance that Michael received
= 2 u
= 2 x 340
= $680

Answers: (a) $1423; (b) $680