Simon and Gabriel were given some allowances each. If Simon spent $16 each day and Gabriel spent $32 each day, Simon would still have $814 left when Gabriel spent all his allowance. If Simon spent $32 each day and Gabriel spent $16 each day, Simon would still have $46 left when Gabriel spent all his allowance.

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

	Case 1		Case 2
	Simon	Gabriel	Simon	Gabriel
Before	1 u + 814	2 u	2 p + 46	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	814	0	46	0

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

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

1 p = 2 u
2 p = 4 u

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

4 u + 46 = 1 u + 814
4 u - 1 u = 814 - 46
3 u = 768

1 u = 768 ÷ 3 = 256

Allowance that Simon received
= 1 u + 814
= 256 + 814
= $1070

(b)
Allowance that Gabriel received
= 2 u
= 2 x 256
= $512

Answers: (a) $1070; (b) $512