Owen and Luke were given some allowances each. If Owen spent $25 each day and Luke spent $75 each day, Owen would still have $2696 left when Luke spent all his allowance. If Owen spent $75 each day and Luke spent $25 each day, Owen would still have $96 left when Luke spent all his allowance.

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

	Case 1		Case 2
	Owen	Luke	Owen	Luke
Before	1 u + 2696	3 u	3 p + 96	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2696	0	96	0

(a)
Simplify the ratio.
25 : 75 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 96 = 1 u + 2696
9 u - 1 u = 2696 - 96
8 u = 2600

1 u = 2600 ÷ 8 = 325

Allowance that Owen received
= 1 u + 2696
= 325 + 2696
= $3021

(b)
Allowance that Luke received
= 3 u
= 3 x 325
= $975

Answers: (a) $3021; (b) $975