Ethan and Albert were given some allowances each. If Ethan spent $16 each day and Albert spent $32 each day, Ethan would still have $812 left when Albert spent all his allowance. If Ethan spent $32 each day and Albert spent $16 each day, Ethan would still have $92 left when Albert spent all his allowance.

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

	Case 1		Case 2
	Ethan	Albert	Ethan	Albert
Before	1 u + 812	2 u	2 p + 92	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	812	0	92	0

(a)
Simplify the ratio.
16 : 32 = 1 : 2

The allowance that Albert 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 + 92 = 1 u + 812
4 u - 1 u = 812 - 92
3 u = 720

1 u = 720 ÷ 3 = 240

Allowance that Ethan received
= 1 u + 812
= 240 + 812
= $1052

(b)
Allowance that Albert received
= 2 u
= 2 x 240
= $480

Answers: (a) $1052; (b) $480