John and Howard were given some allowances each. If John spent $18 each day and Howard spent $54 each day, John would still have $2195 left when Howard spent all his allowance. If John spent $54 each day and Howard spent $18 each day, John would still have $35 left when Howard spent all his allowance.

1. How much allowance did John receive?
2. How much allowance did Howard receive?

	Case 1		Case 2
	John	Howard	John	Howard
Before	1 u + 2195	3 u	3 p + 35	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2195	0	35	0

(a)
Simplify the ratio.
18 : 54 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 35 = 1 u + 2195
9 u - 1 u = 2195 - 35
8 u = 2160

1 u = 2160 ÷ 8 = 270

Allowance that John received
= 1 u + 2195
= 270 + 2195
= $2465

(b)
Allowance that Howard received
= 3 u
= 3 x 270
= $810

Answers: (a) $2465; (b) $810