Fred and Valen were given some allowances each. If Fred spent $25 each day and Valen spent $50 each day, Fred would still have $663 left when Valen spent all his allowance. If Fred spent $50 each day and Valen spent $25 each day, Fred would still have $63 left when Valen spent all his allowance.

1. How much allowance did Fred receive?
2. How much allowance did Valen receive?

	Case 1		Case 2
	Fred	Valen	Fred	Valen
Before	1 u + 663	2 u	2 p + 63	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	663	0	63	0

(a)
Simplify the ratio.
25 : 50 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 63 = 1 u + 663
4 u - 1 u = 663 - 63
3 u = 600

1 u = 600 ÷ 3 = 200

Allowance that Fred received
= 1 u + 663
= 200 + 663
= $863

(b)
Allowance that Valen received
= 2 u
= 2 x 200
= $400

Answers: (a) $863; (b) $400