Xavier and Owen were given some allowances each. If Xavier spent $26 each day and Owen spent $52 each day, Xavier would still have $1115 left when Owen spent all his allowance. If Xavier spent $52 each day and Owen spent $26 each day, Xavier would still have $23 left when Owen spent all his allowance.

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

	Case 1		Case 2
	Xavier	Owen	Xavier	Owen
Before	1 u + 1115	2 u	2 p + 23	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1115	0	23	0

(a)
Simplify the ratio.
26 : 52 = 1 : 2

The allowance that Owen 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 + 23 = 1 u + 1115
4 u - 1 u = 1115 - 23
3 u = 1092

1 u = 1092 ÷ 3 = 364

Allowance that Xavier received
= 1 u + 1115
= 364 + 1115
= $1479

(b)
Allowance that Owen received
= 2 u
= 2 x 364
= $728

Answers: (a) $1479; (b) $728