Fred and Peter were given some allowances each. If Fred spent $10 each day and Peter spent $20 each day, Fred would still have $1117 left when Peter spent all his allowance. If Fred spent $20 each day and Peter spent $10 each day, Fred would still have $37 left when Peter spent all his allowance.

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

	Case 1		Case 2
	Fred	Peter	Fred	Peter
Before	1 u + 1117	2 u	2 p + 37	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1117	0	37	0

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

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

1 p = 2 u
2 p = 4 u

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

4 u + 37 = 1 u + 1117
4 u - 1 u = 1117 - 37
3 u = 1080

1 u = 1080 ÷ 3 = 360

Allowance that Fred received
= 1 u + 1117
= 360 + 1117
= $1477

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

Answers: (a) $1477; (b) $720