Mark and Xavier were given some allowances each. If Mark spent $21 each day and Xavier spent $63 each day, Mark would still have $2566 left when Xavier spent all his allowance. If Mark spent $63 each day and Xavier spent $21 each day, Mark would still have $46 left when Xavier spent all his allowance.

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

	Case 1		Case 2
	Mark	Xavier	Mark	Xavier
Before	1 u + 2566	3 u	3 p + 46	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2566	0	46	0

(a)
Simplify the ratio.
21 : 63 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 46 = 1 u + 2566
9 u - 1 u = 2566 - 46
8 u = 2520

1 u = 2520 ÷ 8 = 315

Allowance that Mark received
= 1 u + 2566
= 315 + 2566
= $2881

(b)
Allowance that Xavier received
= 3 u
= 3 x 315
= $945

Answers: (a) $2881; (b) $945