Ivan and Tim were given some allowances each. If Ivan spent $10 each day and Tim spent $20 each day, Ivan would still have $1104 left when Tim spent all his allowance. If Ivan spent $20 each day and Tim spent $10 each day, Ivan would still have $84 left when Tim spent all his allowance.

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

	Case 1		Case 2
	Ivan	Tim	Ivan	Tim
Before	1 u + 1104	2 u	2 p + 84	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1104	0	84	0

(a)
Simplify the ratio.
10 : 20 = 1 : 2

The allowance that Tim 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 + 84 = 1 u + 1104
4 u - 1 u = 1104 - 84
3 u = 1020

1 u = 1020 ÷ 3 = 340

Allowance that Ivan received
= 1 u + 1104
= 340 + 1104
= $1444

(b)
Allowance that Tim received
= 2 u
= 2 x 340
= $680

Answers: (a) $1444; (b) $680