Pierre and Michael were given some allowances each. If Pierre spent $23 each day and Michael spent $46 each day, Pierre would still have $1234 left when Michael spent all his allowance. If Pierre spent $46 each day and Michael spent $23 each day, Pierre would still have $61 left when Michael spent all his allowance.

1. How much allowance did Pierre receive?
2. How much allowance did Michael receive?

	Case 1		Case 2
	Pierre	Michael	Pierre	Michael
Before	1 u + 1234	2 u	2 p + 61	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1234	0	61	0

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

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

1 p = 2 u
2 p = 4 u

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

4 u + 61 = 1 u + 1234
4 u - 1 u = 1234 - 61
3 u = 1173

1 u = 1173 ÷ 3 = 391

Allowance that Pierre received
= 1 u + 1234
= 391 + 1234
= $1625

(b)
Allowance that Michael received
= 2 u
= 2 x 391
= $782

Answers: (a) $1625; (b) $782