SOLUTION: On a number line, points A, B, and C have coordinates a, b, and c with a < b < c . If b = 6, AC =30, and AB = 2BC , what are the values of a and c?

Algebra ->  Length-and-distance -> SOLUTION: On a number line, points A, B, and C have coordinates a, b, and c with a < b < c . If b = 6, AC =30, and AB = 2BC , what are the values of a and c?      Log On


   

Question 828378: On a number line, points A, B, and C have coordinates a, b, and c with a < b < c . If
b = 6, AC =30, and AB = 2BC , what are the values of a and c?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
 

Given: b = 6, AC = 30, and AB = 2BC

Therefore AB = b-a, BC = c-b, AC = c-a  

 A                   B         C
---------------------------------
a=?                 b=6       c=?

  AB = 2BC                AC = 30
 b-a = 2(c-b)            c-a = 30
 6-a = 2(c-6)
 6-a = 2c-12
  18 = 2c+a
2c+a = 18

So we have the system of two equations in two unknowns:

system%282c%2Ba=18%2Cc-a=30%29

Add the two equations and the a's cancel:

     3c = 48
      c = 16

Substitute in 

   2c+a = 18
2(16)+a = 18
   32+a = 18
      a = -14

Edwin