George and Japheth were given some allowances each. If George spent $10 each day and Japheth spent $20 each day, George would still have $972 left when Japheth spent all his allowance. If George spent $20 each day and Japheth spent $10 each day, George would still have $42 left when Japheth spent all his allowance.

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

	Case 1		Case 2
	George	Japheth	George	Japheth
Before	1 u + 972	2 u	2 p + 42	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	972	0	42	0

(a)
Simplify the ratio.
10 : 20 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 42 = 1 u + 972
4 u - 1 u = 972 - 42
3 u = 930

1 u = 930 ÷ 3 = 310

Allowance that George received
= 1 u + 972
= 310 + 972
= $1282

(b)
Allowance that Japheth received
= 2 u
= 2 x 310
= $620

Answers: (a) $1282; (b) $620