Ben and Sam were given some allowances each. If Ben spent $17 each day and Sam spent $34 each day, Ben would still have $552 left when Sam spent all his allowance. If Ben spent $34 each day and Sam spent $17 each day, Ben would still have $93 left when Sam spent all his allowance.

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

	Case 1		Case 2
	Ben	Sam	Ben	Sam
Before	1 u + 552	2 u	2 p + 93	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	552	0	93	0

(a)
Simplify the ratio.
17 : 34 = 1 : 2

The allowance that Sam 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 + 93 = 1 u + 552
4 u - 1 u = 552 - 93
3 u = 459

1 u = 459 ÷ 3 = 153

Allowance that Ben received
= 1 u + 552
= 153 + 552
= $705

(b)
Allowance that Sam received
= 2 u
= 2 x 153
= $306

Answers: (a) $705; (b) $306