SOLUTION: Use the equations below to find the length of the pipe. (there is a pipe separated into an a, b, and c section) a + b = 15 b - a = 3 a + b - 12 = c How do i set up

Algebra ->  Expressions-with-variables -> SOLUTION: Use the equations below to find the length of the pipe. (there is a pipe separated into an a, b, and c section) a + b = 15 b - a = 3 a + b - 12 = c How do i set up      Log On


   

Question 636896: Use the equations below to find the length of the pipe.
(there is a pipe separated into an a, b, and c section)
a + b = 15
b - a = 3
a + b - 12 = c

How do i set up an equation for this problem?
Thanks!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There are 3 equations and 3 unknowns.
That means this is solvable, since
number of unknowns must equal
number of equations to solve.
------------
(1) +a+%2B+b+=+15+
(2) +b+-+a+=+3+
(3) +a+%2B+b+-+12+=+c+
------------------
(1) +a+=+15+-+b+
Substitute this into (2)
(2) +b+-+%28+15+-+b+%29+=+3+
(2) +b+-+15+%2B+b+=+3+
(2) +2b+=+15+%2B+3+
(2) +2b+=+18+
(2) +b+=+9+
and, since
(1) +a+=+15+-+b+
(1) +a+=+15+-+9+
(1) +a+=+6+
Substitute these results into (3)
(3) +a+%2B+b+-+12+=+c+
(3) +6+%2B+9+-+12+=+c+
(3) +15+-+12+=+c+
(3) +c+=+3+
-----------
+a+=+6+
+b+=+9+
+c+=+3+