Ivan and Gabriel were given some allowances each. If Ivan spent $10 each day and Gabriel spent $30 each day, Ivan would still have $3298 left when Gabriel spent all his allowance. If Ivan spent $30 each day and Gabriel spent $10 each day, Ivan would still have $98 left when Gabriel spent all his allowance.

1. How much allowance did Ivan receive?
2. How much allowance did Gabriel receive?

	Case 1		Case 2
	Ivan	Gabriel	Ivan	Gabriel
Before	1 u + 3298	3 u	3 p + 98	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	3298	0	98	0

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

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

1 p = 3 u
3 p = 9 u

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

9 u + 98 = 1 u + 3298
9 u - 1 u = 3298 - 98
8 u = 3200

1 u = 3200 ÷ 8 = 400

Allowance that Ivan received
= 1 u + 3298
= 400 + 3298
= $3698

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

Answers: (a) $3698; (b) $1200