Xavier and Pierre were given some allowances each. If Xavier spent $25 each day and Pierre spent $50 each day, Xavier would still have $1073 left when Pierre spent all his allowance. If Xavier spent $50 each day and Pierre spent $25 each day, Xavier would still have $98 left when Pierre spent all his allowance.

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

	Case 1		Case 2
	Xavier	Pierre	Xavier	Pierre
Before	1 u + 1073	2 u	2 p + 98	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1073	0	98	0

(a)
Simplify the ratio.
25 : 50 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 98 = 1 u + 1073
4 u - 1 u = 1073 - 98
3 u = 975

1 u = 975 ÷ 3 = 325

Allowance that Xavier received
= 1 u + 1073
= 325 + 1073
= $1398

(b)
Allowance that Pierre received
= 2 u
= 2 x 325
= $650

Answers: (a) $1398; (b) $650