Oliver and Vaidev were given some allowances each. If Oliver spent $10 each day and Vaidev spent $30 each day, Oliver would still have $1216 left when Vaidev spent all his allowance. If Oliver spent $30 each day and Vaidev spent $10 each day, Oliver would still have $96 left when Vaidev spent all his allowance.

1. How much allowance did Oliver receive?
2. How much allowance did Vaidev receive?

	Case 1		Case 2
	Oliver	Vaidev	Oliver	Vaidev
Before	1 u + 1216	3 u	3 p + 96	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1216	0	96	0

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

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

1 p = 3 u
3 p = 9 u

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

9 u + 96 = 1 u + 1216
9 u - 1 u = 1216 - 96
8 u = 1120

1 u = 1120 ÷ 8 = 140

Allowance that Oliver received
= 1 u + 1216
= 140 + 1216
= $1356

(b)
Allowance that Vaidev received
= 3 u
= 3 x 140
= $420

Answers: (a) $1356; (b) $420