Ivan and Jeremy were given some allowances each. If Ivan spent $17 each day and Jeremy spent $34 each day, Ivan would still have $387 left when Jeremy spent all his allowance. If Ivan spent $34 each day and Jeremy spent $17 each day, Ivan would still have $30 left when Jeremy spent all his allowance.

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

	Case 1		Case 2
	Ivan	Jeremy	Ivan	Jeremy
Before	1 u + 387	2 u	2 p + 30	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	387	0	30	0

(a)
Simplify the ratio.
17 : 34 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 30 = 1 u + 387
4 u - 1 u = 387 - 30
3 u = 357

1 u = 357 ÷ 3 = 119

Allowance that Ivan received
= 1 u + 387
= 119 + 387
= $506

(b)
Allowance that Jeremy received
= 2 u
= 2 x 119
= $238

Answers: (a) $506; (b) $238