Question 49204
Let us draw line and mark points A, C and inbetween point B as below :

    A_______________B________________________C
                                          
        
Note that  point B is between A & C but we dont know exactly how many units from either A or C....its ok no prob. We have to find out distance BC...fine..

Let us put the problem statement into equation as below:

AB = 2X-3
BC = 3X+1
AC = 7X-8

From the above line we know that :

AC = AB + BC

Now substitute the values interms of "X" as below,

(7X-8) = (2X-3) + (3X+1)
7X-8 = 2X - 3 + 3X +1 = 5X-2

7X - 5X = 8 - 2 

2X = 6

X = 6/2 = 3

Now we want to know BC = ?

We know that:

BC = 3X+1 here substitute the value of "X" to get distance BC,

BC = 3*3 + 1 = 9+1 = 10 this is the answer.

You can verify the answer as below :

AC = AB + BC
(7X-8) = (2X-3) + (3X+1) Substitute the values of X=3 and see that LHS = RHS of the equation. let us do that,

7*3-8 = 2*3-3 + 3*3+1
21-8 = 6-3+9+1
13 = 13 ( LHS = RHS )

Which means value of X=3 is correct.

Thats all....
B.Shridhar