Fabian and Sam were given some allowances each. If Fabian spent $11 each day and Sam spent $22 each day, Fabian would still have $947 left when Sam spent all his allowance. If Fabian spent $22 each day and Sam spent $11 each day, Fabian would still have $23 left when Sam spent all his allowance.

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

	Case 1		Case 2
	Fabian	Sam	Fabian	Sam
Before	1 u + 947	2 u	2 p + 23	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	947	0	23	0

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

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

1 p = 2 u
2 p = 4 u

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

4 u + 23 = 1 u + 947
4 u - 1 u = 947 - 23
3 u = 924

1 u = 924 ÷ 3 = 308

Allowance that Fabian received
= 1 u + 947
= 308 + 947
= $1255

(b)
Allowance that Sam received
= 2 u
= 2 x 308
= $616

Answers: (a) $1255; (b) $616