Sean and Ethan were given some allowances each. If Sean spent $21 each day and Ethan spent $42 each day, Sean would still have $653 left when Ethan spent all his allowance. If Sean spent $42 each day and Ethan spent $21 each day, Sean would still have $86 left when Ethan spent all his allowance.

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

	Case 1		Case 2
	Sean	Ethan	Sean	Ethan
Before	1 u + 653	2 u	2 p + 86	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	653	0	86	0

(a)
Simplify the ratio.
21 : 42 = 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 Sean had at first is the same for Case 1 and Case 2.

4 u + 86 = 1 u + 653
4 u - 1 u = 653 - 86
3 u = 567

1 u = 567 ÷ 3 = 189

Allowance that Sean received
= 1 u + 653
= 189 + 653
= $842

(b)
Allowance that Ethan received
= 2 u
= 2 x 189
= $378

Answers: (a) $842; (b) $378