Caden and Owen were given some allowances each. If Caden spent $16 each day and Owen spent $48 each day, Caden would still have $1576 left when Owen spent all his allowance. If Caden spent $48 each day and Owen spent $16 each day, Caden would still have $40 left when Owen spent all his allowance.

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

	Case 1		Case 2
	Caden	Owen	Caden	Owen
Before	1 u + 1576	3 u	3 p + 40	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1576	0	40	0

(a)
Simplify the ratio.
16 : 48 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 40 = 1 u + 1576
9 u - 1 u = 1576 - 40
8 u = 1536

1 u = 1536 ÷ 8 = 192

Allowance that Caden received
= 1 u + 1576
= 192 + 1576
= $1768

(b)
Allowance that Owen received
= 3 u
= 3 x 192
= $576

Answers: (a) $1768; (b) $576