Ken and Ethan were given some allowances each. If Ken spent $10 each day and Ethan spent $20 each day, Ken would still have $762 left when Ethan spent all his allowance. If Ken spent $20 each day and Ethan spent $10 each day, Ken would still have $72 left when Ethan spent all his allowance.

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

	Case 1		Case 2
	Ken	Ethan	Ken	Ethan
Before	1 u + 762	2 u	2 p + 72	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	762	0	72	0

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

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

1 p = 2 u
2 p = 4 u

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

4 u + 72 = 1 u + 762
4 u - 1 u = 762 - 72
3 u = 690

1 u = 690 ÷ 3 = 230

Allowance that Ken received
= 1 u + 762
= 230 + 762
= $992

(b)
Allowance that Ethan received
= 2 u
= 2 x 230
= $460

Answers: (a) $992; (b) $460