Vaidev and Billy were given some allowances each. If Vaidev spent $18 each day and Billy spent $54 each day, Vaidev would still have $1193 left when Billy spent all his allowance. If Vaidev spent $54 each day and Billy spent $18 each day, Vaidev would still have $41 left when Billy spent all his allowance.

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

	Case 1		Case 2
	Vaidev	Billy	Vaidev	Billy
Before	1 u + 1193	3 u	3 p + 41	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1193	0	41	0

(a)
Simplify the ratio.
18 : 54 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 41 = 1 u + 1193
9 u - 1 u = 1193 - 41
8 u = 1152

1 u = 1152 ÷ 8 = 144

Allowance that Vaidev received
= 1 u + 1193
= 144 + 1193
= $1337

(b)
Allowance that Billy received
= 3 u
= 3 x 144
= $432

Answers: (a) $1337; (b) $432