Vincent and Neave were given some allowances each. If Vincent spent $15 each day and Neave spent $30 each day, Vincent would still have $870 left when Neave spent all his allowance. If Vincent spent $30 each day and Neave spent $15 each day, Vincent would still have $60 left when Neave spent all his allowance.

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

	Case 1		Case 2
	Vincent	Neave	Vincent	Neave
Before	1 u + 870	2 u	2 p + 60	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	870	0	60	0

(a)
Simplify the ratio.
15 : 30 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 60 = 1 u + 870
4 u - 1 u = 870 - 60
3 u = 810

1 u = 810 ÷ 3 = 270

Allowance that Vincent received
= 1 u + 870
= 270 + 870
= $1140

(b)
Allowance that Neave received
= 2 u
= 2 x 270
= $540

Answers: (a) $1140; (b) $540