John and Billy were given some allowances each. If John spent $30 each day and Billy spent $90 each day, John would still have $2714 left when Billy spent all his allowance. If John spent $90 each day and Billy spent $30 each day, John would still have $74 left when Billy spent all his allowance.

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

	Case 1		Case 2
	John	Billy	John	Billy
Before	1 u + 2714	3 u	3 p + 74	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2714	0	74	0

(a)
Simplify the ratio.
30 : 90 = 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 John had at first is the same for Case 1 and Case 2.

9 u + 74 = 1 u + 2714
9 u - 1 u = 2714 - 74
8 u = 2640

1 u = 2640 ÷ 8 = 330

Allowance that John received
= 1 u + 2714
= 330 + 2714
= $3044

(b)
Allowance that Billy received
= 3 u
= 3 x 330
= $990

Answers: (a) $3044; (b) $990