Cody and Warren were given some allowances each. If Cody spent $18 each day and Warren spent $54 each day, Cody would still have $2970 left when Warren spent all his allowance. If Cody spent $54 each day and Warren spent $18 each day, Cody would still have $90 left when Warren spent all his allowance.

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

	Case 1		Case 2
	Cody	Warren	Cody	Warren
Before	1 u + 2970	3 u	3 p + 90	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2970	0	90	0

(a)
Simplify the ratio.
18 : 54 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 90 = 1 u + 2970
9 u - 1 u = 2970 - 90
8 u = 2880

1 u = 2880 ÷ 8 = 360

Allowance that Cody received
= 1 u + 2970
= 360 + 2970
= $3330

(b)
Allowance that Warren received
= 3 u
= 3 x 360
= $1080

Answers: (a) $3330; (b) $1080