SOLUTION: B is between A and C. AB = 2x - 3, BC = 3x + 1, AC = 7x - 8, find BC. I received a worksheet on the 2nd day of school. Please help I dont know where to begin with this one. T

Question 49204: B is between A and C. AB = 2x - 3, BC = 3x + 1, AC = 7x - 8, find BC.
I received a worksheet on the 2nd day of school. Please help I dont know where to begin with this one.
Thanks
Answer by Osran_Shri(18) (Show Source): You can put this solution on YOUR website!
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

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