Tom and Cody were given some allowances each. If Tom spent $19 each day and Cody spent $38 each day, Tom would still have $773 left when Cody spent all his allowance. If Tom spent $38 each day and Cody spent $19 each day, Tom would still have $89 left when Cody spent all his allowance.

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

	Case 1		Case 2
	Tom	Cody	Tom	Cody
Before	1 u + 773	2 u	2 p + 89	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	773	0	89	0

(a)
Simplify the ratio.
19 : 38 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 89 = 1 u + 773
4 u - 1 u = 773 - 89
3 u = 684

1 u = 684 ÷ 3 = 228

Allowance that Tom received
= 1 u + 773
= 228 + 773
= $1001

(b)
Allowance that Cody received
= 2 u
= 2 x 228
= $456

Answers: (a) $1001; (b) $456