Pierre and Riordan were given some allowances each. If Pierre spent $19 each day and Riordan spent $38 each day, Pierre would still have $707 left when Riordan spent all his allowance. If Pierre spent $38 each day and Riordan spent $19 each day, Pierre would still have $23 left when Riordan spent all his allowance.

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

	Case 1		Case 2
	Pierre	Riordan	Pierre	Riordan
Before	1 u + 707	2 u	2 p + 23	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	707	0	23	0

(a)
Simplify the ratio.
19 : 38 = 1 : 2

The allowance that Riordan 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 + 23 = 1 u + 707
4 u - 1 u = 707 - 23
3 u = 684

1 u = 684 ÷ 3 = 228

Allowance that Pierre received
= 1 u + 707
= 228 + 707
= $935

(b)
Allowance that Riordan received
= 2 u
= 2 x 228
= $456

Answers: (a) $935; (b) $456