Carl and Sean were given some allowances each. If Carl spent $27 each day and Sean spent $54 each day, Carl would still have $720 left when Sean spent all his allowance. If Carl spent $54 each day and Sean spent $27 each day, Carl would still have $72 left when Sean spent all his allowance.

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

	Case 1		Case 2
	Carl	Sean	Carl	Sean
Before	1 u + 720	2 u	2 p + 72	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	720	0	72	0

(a)
Simplify the ratio.
27 : 54 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 72 = 1 u + 720
4 u - 1 u = 720 - 72
3 u = 648

1 u = 648 ÷ 3 = 216

Allowance that Carl received
= 1 u + 720
= 216 + 720
= $936

(b)
Allowance that Sean received
= 2 u
= 2 x 216
= $432

Answers: (a) $936; (b) $432