Jack and Ahmad were given some allowances each. If Jack spent $21 each day and Ahmad spent $63 each day, Jack would still have $1234 left when Ahmad spent all his allowance. If Jack spent $63 each day and Ahmad spent $21 each day, Jack would still have $58 left when Ahmad spent all his allowance.

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

	Case 1		Case 2
	Jack	Ahmad	Jack	Ahmad
Before	1 u + 1234	3 u	3 p + 58	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1234	0	58	0

(a)
Simplify the ratio.
21 : 63 = 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 Jack had at first is the same for Case 1 and Case 2.

9 u + 58 = 1 u + 1234
9 u - 1 u = 1234 - 58
8 u = 1176

1 u = 1176 ÷ 8 = 147

Allowance that Jack received
= 1 u + 1234
= 147 + 1234
= $1381

(b)
Allowance that Ahmad received
= 3 u
= 3 x 147
= $441

Answers: (a) $1381; (b) $441