Sam and Tim were given some allowances each. If Sam spent $28 each day and Tim spent $56 each day, Sam would still have $548 left when Tim spent all his allowance. If Sam spent $56 each day and Tim spent $28 each day, Sam would still have $44 left when Tim spent all his allowance.

1. How much allowance did Sam receive?
2. How much allowance did Tim receive?

	Case 1		Case 2
	Sam	Tim	Sam	Tim
Before	1 u + 548	2 u	2 p + 44	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	548	0	44	0

(a)
Simplify the ratio.
28 : 56 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 44 = 1 u + 548
4 u - 1 u = 548 - 44
3 u = 504

1 u = 504 ÷ 3 = 168

Allowance that Sam received
= 1 u + 548
= 168 + 548
= $716

(b)
Allowance that Tim received
= 2 u
= 2 x 168
= $336

Answers: (a) $716; (b) $336