Luke and Gabriel were given some allowances each. If Luke spent $20 each day and Gabriel spent $40 each day, Luke would still have $1267 left when Gabriel spent all his allowance. If Luke spent $40 each day and Gabriel spent $20 each day, Luke would still have $67 left when Gabriel spent all his allowance.

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

	Case 1		Case 2
	Luke	Gabriel	Luke	Gabriel
Before	1 u + 1267	2 u	2 p + 67	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1267	0	67	0

(a)
Simplify the ratio.
20 : 40 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 67 = 1 u + 1267
4 u - 1 u = 1267 - 67
3 u = 1200

1 u = 1200 ÷ 3 = 400

Allowance that Luke received
= 1 u + 1267
= 400 + 1267
= $1667

(b)
Allowance that Gabriel received
= 2 u
= 2 x 400
= $800

Answers: (a) $1667; (b) $800