Ben and Ethan were given some allowances each. If Ben spent $22 each day and Ethan spent $44 each day, Ben would still have $1237 left when Ethan spent all his allowance. If Ben spent $44 each day and Ethan spent $22 each day, Ben would still have $49 left when Ethan spent all his allowance.

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

	Case 1		Case 2
	Ben	Ethan	Ben	Ethan
Before	1 u + 1237	2 u	2 p + 49	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1237	0	49	0

(a)
Simplify the ratio.
22 : 44 = 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 Ben had at first is the same for Case 1 and Case 2.

4 u + 49 = 1 u + 1237
4 u - 1 u = 1237 - 49
3 u = 1188

1 u = 1188 ÷ 3 = 396

Allowance that Ben received
= 1 u + 1237
= 396 + 1237
= $1633

(b)
Allowance that Ethan received
= 2 u
= 2 x 396
= $792

Answers: (a) $1633; (b) $792