Zane and Oscar were given some allowances each. If Zane spent $10 each day and Oscar spent $30 each day, Zane would still have $3258 left when Oscar spent all his allowance. If Zane spent $30 each day and Oscar spent $10 each day, Zane would still have $58 left when Oscar spent all his allowance.

1. How much allowance did Zane receive?
2. How much allowance did Oscar receive?

	Case 1		Case 2
	Zane	Oscar	Zane	Oscar
Before	1 u + 3258	3 u	3 p + 58	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	3258	0	58	0

(a)
Simplify the ratio.
10 : 30 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 58 = 1 u + 3258
9 u - 1 u = 3258 - 58
8 u = 3200

1 u = 3200 ÷ 8 = 400

Allowance that Zane received
= 1 u + 3258
= 400 + 3258
= $3658

(b)
Allowance that Oscar received
= 3 u
= 3 x 400
= $1200

Answers: (a) $3658; (b) $1200