Daniel and Mark were given some allowances each. If Daniel spent $23 each day and Mark spent $46 each day, Daniel would still have $855 left when Mark spent all his allowance. If Daniel spent $46 each day and Mark spent $23 each day, Daniel would still have $96 left when Mark spent all his allowance.

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

	Case 1		Case 2
	Daniel	Mark	Daniel	Mark
Before	1 u + 855	2 u	2 p + 96	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	855	0	96	0

(a)
Simplify the ratio.
23 : 46 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 96 = 1 u + 855
4 u - 1 u = 855 - 96
3 u = 759

1 u = 759 ÷ 3 = 253

Allowance that Daniel received
= 1 u + 855
= 253 + 855
= $1108

(b)
Allowance that Mark received
= 2 u
= 2 x 253
= $506

Answers: (a) $1108; (b) $506