Mark and Cody were given some allowances each. If Mark spent $27 each day and Cody spent $81 each day, Mark would still have $2630 left when Cody spent all his allowance. If Mark spent $81 each day and Cody spent $27 each day, Mark would still have $38 left when Cody spent all his allowance.

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

	Case 1		Case 2
	Mark	Cody	Mark	Cody
Before	1 u + 2630	3 u	3 p + 38	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2630	0	38	0

(a)
Simplify the ratio.
27 : 81 = 1 : 3

The allowance that Cody 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 + 38 = 1 u + 2630
9 u - 1 u = 2630 - 38
8 u = 2592

1 u = 2592 ÷ 8 = 324

Allowance that Mark received
= 1 u + 2630
= 324 + 2630
= $2954

(b)
Allowance that Cody received
= 3 u
= 3 x 324
= $972

Answers: (a) $2954; (b) $972