Harry and Fred were given some allowances each. If Harry spent $18 each day and Fred spent $36 each day, Harry would still have $917 left when Fred spent all his allowance. If Harry spent $36 each day and Fred spent $18 each day, Harry would still have $53 left when Fred spent all his allowance.

1. How much allowance did Harry receive?
2. How much allowance did Fred receive?

	Case 1		Case 2
	Harry	Fred	Harry	Fred
Before	1 u + 917	2 u	2 p + 53	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	917	0	53	0

(a)
Simplify the ratio.
18 : 36 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 53 = 1 u + 917
4 u - 1 u = 917 - 53
3 u = 864

1 u = 864 ÷ 3 = 288

Allowance that Harry received
= 1 u + 917
= 288 + 917
= $1205

(b)
Allowance that Fred received
= 2 u
= 2 x 288
= $576

Answers: (a) $1205; (b) $576