Ian and Howard were given some allowances each. If Ian spent $29 each day and Howard spent $58 each day, Ian would still have $737 left when Howard spent all his allowance. If Ian spent $58 each day and Howard spent $29 each day, Ian would still have $41 left when Howard spent all his allowance.

1. How much allowance did Ian receive?
2. How much allowance did Howard receive?

	Case 1		Case 2
	Ian	Howard	Ian	Howard
Before	1 u + 737	2 u	2 p + 41	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	737	0	41	0

(a)
Simplify the ratio.
29 : 58 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 41 = 1 u + 737
4 u - 1 u = 737 - 41
3 u = 696

1 u = 696 ÷ 3 = 232

Allowance that Ian received
= 1 u + 737
= 232 + 737
= $969

(b)
Allowance that Howard received
= 2 u
= 2 x 232
= $464

Answers: (a) $969; (b) $464