Elijah and Archie were given some allowances each. If Elijah spent $30 each day and Archie spent $60 each day, Elijah would still have $453 left when Archie spent all his allowance. If Elijah spent $60 each day and Archie spent $30 each day, Elijah would still have $93 left when Archie spent all his allowance.

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

	Case 1		Case 2
	Elijah	Archie	Elijah	Archie
Before	1 u + 453	2 u	2 p + 93	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	453	0	93	0

(a)
Simplify the ratio.
30 : 60 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 93 = 1 u + 453
4 u - 1 u = 453 - 93
3 u = 360

1 u = 360 ÷ 3 = 120

Allowance that Elijah received
= 1 u + 453
= 120 + 453
= $573

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

Answers: (a) $573; (b) $240