Tim and Michael were given some allowances each. If Tim spent $15 each day and Michael spent $30 each day, Tim would still have $1135 left when Michael spent all his allowance. If Tim spent $30 each day and Michael spent $15 each day, Tim would still have $55 left when Michael spent all his allowance.

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

	Case 1		Case 2
	Tim	Michael	Tim	Michael
Before	1 u + 1135	2 u	2 p + 55	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1135	0	55	0

(a)
Simplify the ratio.
15 : 30 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 55 = 1 u + 1135
4 u - 1 u = 1135 - 55
3 u = 1080

1 u = 1080 ÷ 3 = 360

Allowance that Tim received
= 1 u + 1135
= 360 + 1135
= $1495

(b)
Allowance that Michael received
= 2 u
= 2 x 360
= $720

Answers: (a) $1495; (b) $720