Pierre and Justin were given some allowances each. If Pierre spent $13 each day and Justin spent $26 each day, Pierre would still have $728 left when Justin spent all his allowance. If Pierre spent $26 each day and Justin spent $13 each day, Pierre would still have $26 left when Justin spent all his allowance.

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

	Case 1		Case 2
	Pierre	Justin	Pierre	Justin
Before	1 u + 728	2 u	2 p + 26	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	728	0	26	0

(a)
Simplify the ratio.
13 : 26 = 1 : 2

The allowance that Justin 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 + 26 = 1 u + 728
4 u - 1 u = 728 - 26
3 u = 702

1 u = 702 ÷ 3 = 234

Allowance that Pierre received
= 1 u + 728
= 234 + 728
= $962

(b)
Allowance that Justin received
= 2 u
= 2 x 234
= $468

Answers: (a) $962; (b) $468