Sam and Ahmad were given some allowances each. If Sam spent $24 each day and Ahmad spent $48 each day, Sam would still have $1233 left when Ahmad spent all his allowance. If Sam spent $48 each day and Ahmad spent $24 each day, Sam would still have $81 left when Ahmad spent all his allowance.

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

	Case 1		Case 2
	Sam	Ahmad	Sam	Ahmad
Before	1 u + 1233	2 u	2 p + 81	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1233	0	81	0

(a)
Simplify the ratio.
24 : 48 = 1 : 2

The allowance that Ahmad 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 + 81 = 1 u + 1233
4 u - 1 u = 1233 - 81
3 u = 1152

1 u = 1152 ÷ 3 = 384

Allowance that Sam received
= 1 u + 1233
= 384 + 1233
= $1617

(b)
Allowance that Ahmad received
= 2 u
= 2 x 384
= $768

Answers: (a) $1617; (b) $768