Luke and Luis were given some allowances each. If Luke spent $26 each day and Luis spent $52 each day, Luke would still have $697 left when Luis spent all his allowance. If Luke spent $52 each day and Luis spent $26 each day, Luke would still have $73 left when Luis spent all his allowance.

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

	Case 1		Case 2
	Luke	Luis	Luke	Luis
Before	1 u + 697	2 u	2 p + 73	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	697	0	73	0

(a)
Simplify the ratio.
26 : 52 = 1 : 2

The allowance that Luis 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 + 73 = 1 u + 697
4 u - 1 u = 697 - 73
3 u = 624

1 u = 624 ÷ 3 = 208

Allowance that Luke received
= 1 u + 697
= 208 + 697
= $905

(b)
Allowance that Luis received
= 2 u
= 2 x 208
= $416

Answers: (a) $905; (b) $416