Jack and Pierre were given some allowances each. If Jack spent $13 each day and Pierre spent $26 each day, Jack would still have $867 left when Pierre spent all his allowance. If Jack spent $26 each day and Pierre spent $13 each day, Jack would still have $87 left when Pierre spent all his allowance.

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

	Case 1		Case 2
	Jack	Pierre	Jack	Pierre
Before	1 u + 867	2 u	2 p + 87	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	867	0	87	0

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

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

1 p = 2 u
2 p = 4 u

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

4 u + 87 = 1 u + 867
4 u - 1 u = 867 - 87
3 u = 780

1 u = 780 ÷ 3 = 260

Allowance that Jack received
= 1 u + 867
= 260 + 867
= $1127

(b)
Allowance that Pierre received
= 2 u
= 2 x 260
= $520

Answers: (a) $1127; (b) $520