Luke and Pierre were given some allowances each. If Luke spent $24 each day and Pierre spent $72 each day, Luke would still have $2346 left when Pierre spent all his allowance. If Luke spent $72 each day and Pierre spent $24 each day, Luke would still have $42 left when Pierre spent all his allowance.

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

	Case 1		Case 2
	Luke	Pierre	Luke	Pierre
Before	1 u + 2346	3 u	3 p + 42	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2346	0	42	0

(a)
Simplify the ratio.
24 : 72 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 42 = 1 u + 2346
9 u - 1 u = 2346 - 42
8 u = 2304

1 u = 2304 ÷ 8 = 288

Allowance that Luke received
= 1 u + 2346
= 288 + 2346
= $2634

(b)
Allowance that Pierre received
= 3 u
= 3 x 288
= $864

Answers: (a) $2634; (b) $864