Owen and Neave were given some allowances each. If Owen spent $17 each day and Neave spent $51 each day, Owen would still have $1407 left when Neave spent all his allowance. If Owen spent $51 each day and Neave spent $17 each day, Owen would still have $47 left when Neave spent all his allowance.

1. How much allowance did Owen receive?
2. How much allowance did Neave receive?

	Case 1		Case 2
	Owen	Neave	Owen	Neave
Before	1 u + 1407	3 u	3 p + 47	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1407	0	47	0

(a)
Simplify the ratio.
17 : 51 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 47 = 1 u + 1407
9 u - 1 u = 1407 - 47
8 u = 1360

1 u = 1360 ÷ 8 = 170

Allowance that Owen received
= 1 u + 1407
= 170 + 1407
= $1577

(b)
Allowance that Neave received
= 3 u
= 3 x 170
= $510

Answers: (a) $1577; (b) $510