Xavier and Asher were given some allowances each. If Xavier spent $19 each day and Asher spent $57 each day, Xavier would still have $2804 left when Asher spent all his allowance. If Xavier spent $57 each day and Asher spent $19 each day, Xavier would still have $68 left when Asher spent all his allowance.

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

	Case 1		Case 2
	Xavier	Asher	Xavier	Asher
Before	1 u + 2804	3 u	3 p + 68	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2804	0	68	0

(a)
Simplify the ratio.
19 : 57 = 1 : 3

The allowance that Asher 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 + 68 = 1 u + 2804
9 u - 1 u = 2804 - 68
8 u = 2736

1 u = 2736 ÷ 8 = 342

Allowance that Xavier received
= 1 u + 2804
= 342 + 2804
= $3146

(b)
Allowance that Asher received
= 3 u
= 3 x 342
= $1026

Answers: (a) $3146; (b) $1026