Gabriel and Ethan were given some allowances each. If Gabriel spent $17 each day and Ethan spent $34 each day, Gabriel would still have $661 left when Ethan spent all his allowance. If Gabriel spent $34 each day and Ethan spent $17 each day, Gabriel would still have $49 left when Ethan spent all his allowance.

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

	Case 1		Case 2
	Gabriel	Ethan	Gabriel	Ethan
Before	1 u + 661	2 u	2 p + 49	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	661	0	49	0

(a)
Simplify the ratio.
17 : 34 = 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 Gabriel had at first is the same for Case 1 and Case 2.

4 u + 49 = 1 u + 661
4 u - 1 u = 661 - 49
3 u = 612

1 u = 612 ÷ 3 = 204

Allowance that Gabriel received
= 1 u + 661
= 204 + 661
= $865

(b)
Allowance that Ethan received
= 2 u
= 2 x 204
= $408

Answers: (a) $865; (b) $408