Billy and Ken were given some allowances each. If Billy spent $11 each day and Ken spent $33 each day, Billy would still have $2472 left when Ken spent all his allowance. If Billy spent $33 each day and Ken spent $11 each day, Billy would still have $96 left when Ken spent all his allowance.

1. How much allowance did Billy receive?
2. How much allowance did Ken receive?

	Case 1		Case 2
	Billy	Ken	Billy	Ken
Before	1 u + 2472	3 u	3 p + 96	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2472	0	96	0

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

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

1 p = 3 u
3 p = 9 u

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

9 u + 96 = 1 u + 2472
9 u - 1 u = 2472 - 96
8 u = 2376

1 u = 2376 ÷ 8 = 297

Allowance that Billy received
= 1 u + 2472
= 297 + 2472
= $2769

(b)
Allowance that Ken received
= 3 u
= 3 x 297
= $891

Answers: (a) $2769; (b) $891