Tim and Vincent were given some allowances each. If Tim spent $20 each day and Vincent spent $40 each day, Tim would still have $1207 left when Vincent spent all his allowance. If Tim spent $40 each day and Vincent spent $20 each day, Tim would still have $67 left when Vincent spent all his allowance.

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

	Case 1		Case 2
	Tim	Vincent	Tim	Vincent
Before	1 u + 1207	2 u	2 p + 67	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1207	0	67	0

(a)
Simplify the ratio.
20 : 40 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 67 = 1 u + 1207
4 u - 1 u = 1207 - 67
3 u = 1140

1 u = 1140 ÷ 3 = 380

Allowance that Tim received
= 1 u + 1207
= 380 + 1207
= $1587

(b)
Allowance that Vincent received
= 2 u
= 2 x 380
= $760

Answers: (a) $1587; (b) $760