Reggie and Ivan were given some allowances each. If Reggie spent $12 each day and Ivan spent $24 each day, Reggie would still have $432 left when Ivan spent all his allowance. If Reggie spent $24 each day and Ivan spent $12 each day, Reggie would still have $72 left when Ivan spent all his allowance.

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

	Case 1		Case 2
	Reggie	Ivan	Reggie	Ivan
Before	1 u + 432	2 u	2 p + 72	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	432	0	72	0

(a)
Simplify the ratio.
12 : 24 = 1 : 2

The allowance that Ivan 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 + 72 = 1 u + 432
4 u - 1 u = 432 - 72
3 u = 360

1 u = 360 ÷ 3 = 120

Allowance that Reggie received
= 1 u + 432
= 120 + 432
= $552

(b)
Allowance that Ivan received
= 2 u
= 2 x 120
= $240

Answers: (a) $552; (b) $240