Tim and Fred were given some allowances each. If Tim spent $21 each day and Fred spent $42 each day, Tim would still have $839 left when Fred spent all his allowance. If Tim spent $42 each day and Fred spent $21 each day, Tim would still have $20 left when Fred spent all his allowance.

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

	Case 1		Case 2
	Tim	Fred	Tim	Fred
Before	1 u + 839	2 u	2 p + 20	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	839	0	20	0

(a)
Simplify the ratio.
21 : 42 = 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 Tim had at first is the same for Case 1 and Case 2.

4 u + 20 = 1 u + 839
4 u - 1 u = 839 - 20
3 u = 819

1 u = 819 ÷ 3 = 273

Allowance that Tim received
= 1 u + 839
= 273 + 839
= $1112

(b)
Allowance that Fred received
= 2 u
= 2 x 273
= $546

Answers: (a) $1112; (b) $546