Sean and Xavier were given some allowances each. If Sean spent $16 each day and Xavier spent $48 each day, Sean would still have $1444 left when Xavier spent all his allowance. If Sean spent $48 each day and Xavier spent $16 each day, Sean would still have $36 left when Xavier spent all his allowance.

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

	Case 1		Case 2
	Sean	Xavier	Sean	Xavier
Before	1 u + 1444	3 u	3 p + 36	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1444	0	36	0

(a)
Simplify the ratio.
16 : 48 = 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 Sean had at first is the same for Case 1 and Case 2.

9 u + 36 = 1 u + 1444
9 u - 1 u = 1444 - 36
8 u = 1408

1 u = 1408 ÷ 8 = 176

Allowance that Sean received
= 1 u + 1444
= 176 + 1444
= $1620

(b)
Allowance that Xavier received
= 3 u
= 3 x 176
= $528

Answers: (a) $1620; (b) $528