Daniel and Tim were given some allowances each. If Daniel spent $20 each day and Tim spent $60 each day, Daniel would still have $2756 left when Tim spent all his allowance. If Daniel spent $60 each day and Tim spent $20 each day, Daniel would still have $36 left when Tim spent all his allowance.

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

	Case 1		Case 2
	Daniel	Tim	Daniel	Tim
Before	1 u + 2756	3 u	3 p + 36	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2756	0	36	0

(a)
Simplify the ratio.
20 : 60 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 36 = 1 u + 2756
9 u - 1 u = 2756 - 36
8 u = 2720

1 u = 2720 ÷ 8 = 340

Allowance that Daniel received
= 1 u + 2756
= 340 + 2756
= $3096

(b)
Allowance that Tim received
= 3 u
= 3 x 340
= $1020

Answers: (a) $3096; (b) $1020