Tom and Neave were given some allowances each. If Tom spent $11 each day and Neave spent $22 each day, Tom would still have $1048 left when Neave spent all his allowance. If Tom spent $22 each day and Neave spent $11 each day, Tom would still have $25 left when Neave spent all his allowance.

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

	Case 1		Case 2
	Tom	Neave	Tom	Neave
Before	1 u + 1048	2 u	2 p + 25	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1048	0	25	0

(a)
Simplify the ratio.
11 : 22 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 25 = 1 u + 1048
4 u - 1 u = 1048 - 25
3 u = 1023

1 u = 1023 ÷ 3 = 341

Allowance that Tom received
= 1 u + 1048
= 341 + 1048
= $1389

(b)
Allowance that Neave received
= 2 u
= 2 x 341
= $682

Answers: (a) $1389; (b) $682