John and Lee were given some allowances each. If John spent $14 each day and Lee spent $42 each day, John would still have $2169 left when Lee spent all his allowance. If John spent $42 each day and Lee spent $14 each day, John would still have $41 left when Lee spent all his allowance.

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

	Case 1		Case 2
	John	Lee	John	Lee
Before	1 u + 2169	3 u	3 p + 41	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2169	0	41	0

(a)
Simplify the ratio.
14 : 42 = 1 : 3

The allowance that Lee 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 + 41 = 1 u + 2169
9 u - 1 u = 2169 - 41
8 u = 2128

1 u = 2128 ÷ 8 = 266

Allowance that John received
= 1 u + 2169
= 266 + 2169
= $2435

(b)
Allowance that Lee received
= 3 u
= 3 x 266
= $798

Answers: (a) $2435; (b) $798