Julian and Billy were given some allowances each. If Julian spent $18 each day and Billy spent $54 each day, Julian would still have $1534 left when Billy spent all his allowance. If Julian spent $54 each day and Billy spent $18 each day, Julian would still have $94 left when Billy spent all his allowance.

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

	Case 1		Case 2
	Julian	Billy	Julian	Billy
Before	1 u + 1534	3 u	3 p + 94	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1534	0	94	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 Julian had at first is the same for Case 1 and Case 2.

9 u + 94 = 1 u + 1534
9 u - 1 u = 1534 - 94
8 u = 1440

1 u = 1440 ÷ 8 = 180

Allowance that Julian received
= 1 u + 1534
= 180 + 1534
= $1714

(b)
Allowance that Billy received
= 3 u
= 3 x 180
= $540

Answers: (a) $1714; (b) $540