Luke and Zane were given some allowances each. If Luke spent $11 each day and Zane spent $33 each day, Luke would still have $2059 left when Zane spent all his allowance. If Luke spent $33 each day and Zane spent $11 each day, Luke would still have $35 left when Zane spent all his allowance.

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

	Case 1		Case 2
	Luke	Zane	Luke	Zane
Before	1 u + 2059	3 u	3 p + 35	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2059	0	35	0

(a)
Simplify the ratio.
11 : 33 = 1 : 3

The allowance that Zane 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 + 35 = 1 u + 2059
9 u - 1 u = 2059 - 35
8 u = 2024

1 u = 2024 ÷ 8 = 253

Allowance that Luke received
= 1 u + 2059
= 253 + 2059
= $2312

(b)
Allowance that Zane received
= 3 u
= 3 x 253
= $759

Answers: (a) $2312; (b) $759