Carl and Vincent were given some allowances each. If Carl spent $17 each day and Vincent spent $34 each day, Carl would still have $632 left when Vincent spent all his allowance. If Carl spent $34 each day and Vincent spent $17 each day, Carl would still have $71 left when Vincent spent all his allowance.

1. How much allowance did Carl receive?
2. How much allowance did Vincent receive?

	Case 1		Case 2
	Carl	Vincent	Carl	Vincent
Before	1 u + 632	2 u	2 p + 71	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	632	0	71	0

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

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

1 p = 2 u
2 p = 4 u

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

4 u + 71 = 1 u + 632
4 u - 1 u = 632 - 71
3 u = 561

1 u = 561 ÷ 3 = 187

Allowance that Carl received
= 1 u + 632
= 187 + 632
= $819

(b)
Allowance that Vincent received
= 2 u
= 2 x 187
= $374

Answers: (a) $819; (b) $374