Justin and Ethan were given some allowances each. If Justin spent $28 each day and Ethan spent $56 each day, Justin would still have $635 left when Ethan spent all his allowance. If Justin spent $56 each day and Ethan spent $28 each day, Justin would still have $47 left when Ethan spent all his allowance.

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

	Case 1		Case 2
	Justin	Ethan	Justin	Ethan
Before	1 u + 635	2 u	2 p + 47	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	635	0	47	0

(a)
Simplify the ratio.
28 : 56 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 47 = 1 u + 635
4 u - 1 u = 635 - 47
3 u = 588

1 u = 588 ÷ 3 = 196

Allowance that Justin received
= 1 u + 635
= 196 + 635
= $831

(b)
Allowance that Ethan received
= 2 u
= 2 x 196
= $392

Answers: (a) $831; (b) $392