Sam and Will were given some allowances each. If Sam spent $21 each day and Will spent $42 each day, Sam would still have $1076 left when Will spent all his allowance. If Sam spent $42 each day and Will spent $21 each day, Sam would still have $68 left when Will spent all his allowance.

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

	Case 1		Case 2
	Sam	Will	Sam	Will
Before	1 u + 1076	2 u	2 p + 68	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1076	0	68	0

(a)
Simplify the ratio.
21 : 42 = 1 : 2

The allowance that Will 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 + 68 = 1 u + 1076
4 u - 1 u = 1076 - 68
3 u = 1008

1 u = 1008 ÷ 3 = 336

Allowance that Sam received
= 1 u + 1076
= 336 + 1076
= $1412

(b)
Allowance that Will received
= 2 u
= 2 x 336
= $672

Answers: (a) $1412; (b) $672