Tom and Luke were given some allowances each. If Tom spent $24 each day and Luke spent $72 each day, Tom would still have $2348 left when Luke spent all his allowance. If Tom spent $72 each day and Luke spent $24 each day, Tom would still have $44 left when Luke spent all his allowance.

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

	Case 1		Case 2
	Tom	Luke	Tom	Luke
Before	1 u + 2348	3 u	3 p + 44	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2348	0	44	0

(a)
Simplify the ratio.
24 : 72 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 44 = 1 u + 2348
9 u - 1 u = 2348 - 44
8 u = 2304

1 u = 2304 ÷ 8 = 288

Allowance that Tom received
= 1 u + 2348
= 288 + 2348
= $2636

(b)
Allowance that Luke received
= 3 u
= 3 x 288
= $864

Answers: (a) $2636; (b) $864