Tommy and Daniel were given some allowances each. If Tommy spent $23 each day and Daniel spent $46 each day, Tommy would still have $1067 left when Daniel spent all his allowance. If Tommy spent $46 each day and Daniel spent $23 each day, Tommy would still have $32 left when Daniel spent all his allowance.

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

	Case 1		Case 2
	Tommy	Daniel	Tommy	Daniel
Before	1 u + 1067	2 u	2 p + 32	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1067	0	32	0

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

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

1 p = 2 u
2 p = 4 u

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

4 u + 32 = 1 u + 1067
4 u - 1 u = 1067 - 32
3 u = 1035

1 u = 1035 ÷ 3 = 345

Allowance that Tommy received
= 1 u + 1067
= 345 + 1067
= $1412

(b)
Allowance that Daniel received
= 2 u
= 2 x 345
= $690

Answers: (a) $1412; (b) $690