John and Eric were given some allowances each. If John spent $15 each day and Eric spent $45 each day, John would still have $2312 left when Eric spent all his allowance. If John spent $45 each day and Eric spent $15 each day, John would still have $32 left when Eric spent all his allowance.

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

	Case 1		Case 2
	John	Eric	John	Eric
Before	1 u + 2312	3 u	3 p + 32	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2312	0	32	0

(a)
Simplify the ratio.
15 : 45 = 1 : 3

The allowance that Eric 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 + 32 = 1 u + 2312
9 u - 1 u = 2312 - 32
8 u = 2280

1 u = 2280 ÷ 8 = 285

Allowance that John received
= 1 u + 2312
= 285 + 2312
= $2597

(b)
Allowance that Eric received
= 3 u
= 3 x 285
= $855

Answers: (a) $2597; (b) $855