Mark and Ivan were given some allowances each. If Mark spent $17 each day and Ivan spent $34 each day, Mark would still have $802 left when Ivan spent all his allowance. If Mark spent $34 each day and Ivan spent $17 each day, Mark would still have $37 left when Ivan spent all his allowance.

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

	Case 1		Case 2
	Mark	Ivan	Mark	Ivan
Before	1 u + 802	2 u	2 p + 37	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	802	0	37	0

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

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

1 p = 2 u
2 p = 4 u

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

4 u + 37 = 1 u + 802
4 u - 1 u = 802 - 37
3 u = 765

1 u = 765 ÷ 3 = 255

Allowance that Mark received
= 1 u + 802
= 255 + 802
= $1057

(b)
Allowance that Ivan received
= 2 u
= 2 x 255
= $510

Answers: (a) $1057; (b) $510