Xavier and Ahmad were given some allowances each. If Xavier spent $14 each day and Ahmad spent $42 each day, Xavier would still have $989 left when Ahmad spent all his allowance. If Xavier spent $42 each day and Ahmad spent $14 each day, Xavier would still have $93 left when Ahmad spent all his allowance.

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

	Case 1		Case 2
	Xavier	Ahmad	Xavier	Ahmad
Before	1 u + 989	3 u	3 p + 93	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	989	0	93	0

(a)
Simplify the ratio.
14 : 42 = 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 Xavier had at first is the same for Case 1 and Case 2.

9 u + 93 = 1 u + 989
9 u - 1 u = 989 - 93
8 u = 896

1 u = 896 ÷ 8 = 112

Allowance that Xavier received
= 1 u + 989
= 112 + 989
= $1101

(b)
Allowance that Ahmad received
= 3 u
= 3 x 112
= $336

Answers: (a) $1101; (b) $336