Caden and Ken were given some allowances each. If Caden spent $18 each day and Ken spent $36 each day, Caden would still have $1006 left when Ken spent all his allowance. If Caden spent $36 each day and Ken spent $18 each day, Caden would still have $34 left when Ken spent all his allowance.

1. How much allowance did Caden receive?
2. How much allowance did Ken receive?

	Case 1		Case 2
	Caden	Ken	Caden	Ken
Before	1 u + 1006	2 u	2 p + 34	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1006	0	34	0

(a)
Simplify the ratio.
18 : 36 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 34 = 1 u + 1006
4 u - 1 u = 1006 - 34
3 u = 972

1 u = 972 ÷ 3 = 324

Allowance that Caden received
= 1 u + 1006
= 324 + 1006
= $1330

(b)
Allowance that Ken received
= 2 u
= 2 x 324
= $648

Answers: (a) $1330; (b) $648