Japheth and Will were given some allowances each. If Japheth spent $10 each day and Will spent $30 each day, Japheth would still have $2492 left when Will spent all his allowance. If Japheth spent $30 each day and Will spent $10 each day, Japheth would still have $92 left when Will spent all his allowance.

1. How much allowance did Japheth receive?
2. How much allowance did Will receive?

	Case 1		Case 2
	Japheth	Will	Japheth	Will
Before	1 u + 2492	3 u	3 p + 92	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2492	0	92	0

(a)
Simplify the ratio.
10 : 30 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 92 = 1 u + 2492
9 u - 1 u = 2492 - 92
8 u = 2400

1 u = 2400 ÷ 8 = 300

Allowance that Japheth received
= 1 u + 2492
= 300 + 2492
= $2792

(b)
Allowance that Will received
= 3 u
= 3 x 300
= $900

Answers: (a) $2792; (b) $900