Billy and Vincent were given some allowances each. If Billy spent $24 each day and Vincent spent $72 each day, Billy would still have $1630 left when Vincent spent all his allowance. If Billy spent $72 each day and Vincent spent $24 each day, Billy would still have $94 left when Vincent spent all his allowance.

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

	Case 1		Case 2
	Billy	Vincent	Billy	Vincent
Before	1 u + 1630	3 u	3 p + 94	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1630	0	94	0

(a)
Simplify the ratio.
24 : 72 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 94 = 1 u + 1630
9 u - 1 u = 1630 - 94
8 u = 1536

1 u = 1536 ÷ 8 = 192

Allowance that Billy received
= 1 u + 1630
= 192 + 1630
= $1822

(b)
Allowance that Vincent received
= 3 u
= 3 x 192
= $576

Answers: (a) $1822; (b) $576