Luke and Neave were given some allowances each. If Luke spent $14 each day and Neave spent $42 each day, Luke would still have $2338 left when Neave spent all his allowance. If Luke spent $42 each day and Neave spent $14 each day, Luke would still have $98 left when Neave spent all his allowance.

1. How much allowance did Luke receive?
2. How much allowance did Neave receive?

	Case 1		Case 2
	Luke	Neave	Luke	Neave
Before	1 u + 2338	3 u	3 p + 98	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2338	0	98	0

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

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

1 p = 3 u
3 p = 9 u

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

9 u + 98 = 1 u + 2338
9 u - 1 u = 2338 - 98
8 u = 2240

1 u = 2240 ÷ 8 = 280

Allowance that Luke received
= 1 u + 2338
= 280 + 2338
= $2618

(b)
Allowance that Neave received
= 3 u
= 3 x 280
= $840

Answers: (a) $2618; (b) $840