Peter and Ahmad were given some allowances each. If Peter spent $19 each day and Ahmad spent $57 each day, Peter would still have $3287 left when Ahmad spent all his allowance. If Peter spent $57 each day and Ahmad spent $19 each day, Peter would still have $95 left when Ahmad spent all his allowance.

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

	Case 1		Case 2
	Peter	Ahmad	Peter	Ahmad
Before	1 u + 3287	3 u	3 p + 95	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	3287	0	95	0

(a)
Simplify the ratio.
19 : 57 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 95 = 1 u + 3287
9 u - 1 u = 3287 - 95
8 u = 3192

1 u = 3192 ÷ 8 = 399

Allowance that Peter received
= 1 u + 3287
= 399 + 3287
= $3686

(b)
Allowance that Ahmad received
= 3 u
= 3 x 399
= $1197

Answers: (a) $3686; (b) $1197