John and Liam were given some allowances each. If John spent $30 each day and Liam spent $90 each day, John would still have $1475 left when Liam spent all his allowance. If John spent $90 each day and Liam spent $30 each day, John would still have $35 left when Liam spent all his allowance.

1. How much allowance did John receive?
2. How much allowance did Liam receive?

	Case 1		Case 2
	John	Liam	John	Liam
Before	1 u + 1475	3 u	3 p + 35	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1475	0	35	0

(a)
Simplify the ratio.
30 : 90 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 35 = 1 u + 1475
9 u - 1 u = 1475 - 35
8 u = 1440

1 u = 1440 ÷ 8 = 180

Allowance that John received
= 1 u + 1475
= 180 + 1475
= $1655

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

Answers: (a) $1655; (b) $540