Rael and Ethan were given some allowances each. If Rael spent $16 each day and Ethan spent $32 each day, Rael would still have $597 left when Ethan spent all his allowance. If Rael spent $32 each day and Ethan spent $16 each day, Rael would still have $21 left when Ethan spent all his allowance.

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

	Case 1		Case 2
	Rael	Ethan	Rael	Ethan
Before	1 u + 597	2 u	2 p + 21	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	597	0	21	0

(a)
Simplify the ratio.
16 : 32 = 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 Rael had at first is the same for Case 1 and Case 2.

4 u + 21 = 1 u + 597
4 u - 1 u = 597 - 21
3 u = 576

1 u = 576 ÷ 3 = 192

Allowance that Rael received
= 1 u + 597
= 192 + 597
= $789

(b)
Allowance that Ethan received
= 2 u
= 2 x 192
= $384

Answers: (a) $789; (b) $384