Ethan and Will were given some allowances each. If Ethan spent $25 each day and Will spent $50 each day, Ethan would still have $404 left when Will spent all his allowance. If Ethan spent $50 each day and Will spent $25 each day, Ethan would still have $29 left when Will spent all his allowance.

1. How much allowance did Ethan receive?
2. How much allowance did Will receive?

	Case 1		Case 2
	Ethan	Will	Ethan	Will
Before	1 u + 404	2 u	2 p + 29	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	404	0	29	0

(a)
Simplify the ratio.
25 : 50 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 29 = 1 u + 404
4 u - 1 u = 404 - 29
3 u = 375

1 u = 375 ÷ 3 = 125

Allowance that Ethan received
= 1 u + 404
= 125 + 404
= $529

(b)
Allowance that Will received
= 2 u
= 2 x 125
= $250

Answers: (a) $529; (b) $250