Vincent and Ian were given some allowances each. If Vincent spent $21 each day and Ian spent $42 each day, Vincent would still have $987 left when Ian spent all his allowance. If Vincent spent $42 each day and Ian spent $21 each day, Vincent would still have $42 left when Ian spent all his allowance.

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

	Case 1		Case 2
	Vincent	Ian	Vincent	Ian
Before	1 u + 987	2 u	2 p + 42	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	987	0	42	0

(a)
Simplify the ratio.
21 : 42 = 1 : 2

The allowance that Ian 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 + 42 = 1 u + 987
4 u - 1 u = 987 - 42
3 u = 945

1 u = 945 ÷ 3 = 315

Allowance that Vincent received
= 1 u + 987
= 315 + 987
= $1302

(b)
Allowance that Ian received
= 2 u
= 2 x 315
= $630

Answers: (a) $1302; (b) $630