Xavier and Reggie were given some allowances each. If Xavier spent $11 each day and Reggie spent $33 each day, Xavier would still have $2511 left when Reggie spent all his allowance. If Xavier spent $33 each day and Reggie spent $11 each day, Xavier would still have $47 left when Reggie spent all his allowance.

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

	Case 1		Case 2
	Xavier	Reggie	Xavier	Reggie
Before	1 u + 2511	3 u	3 p + 47	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2511	0	47	0

(a)
Simplify the ratio.
11 : 33 = 1 : 3

The allowance that Reggie 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 + 47 = 1 u + 2511
9 u - 1 u = 2511 - 47
8 u = 2464

1 u = 2464 ÷ 8 = 308

Allowance that Xavier received
= 1 u + 2511
= 308 + 2511
= $2819

(b)
Allowance that Reggie received
= 3 u
= 3 x 308
= $924

Answers: (a) $2819; (b) $924