SOLUTION: If a and b are integers and 3b*pi+14=12a*pi+7a, find the value of a+b. I know the answer is 10. But don't know how to solve.

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: If a and b are integers and 3b*pi+14=12a*pi+7a, find the value of a+b. I know the answer is 10. But don't know how to solve.      Log On


   

Question 1023415: If a and b are integers and 3b*pi+14=12a*pi+7a, find the value of a+b.
I know the answer is 10. But don't know how to solve.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
3b*pi+14=12a*pi+7a
The terms which are irrational multiples of pi on each side 
must be equal:

3b*pi=12a*pi

The terms which are integers on each side must be equal:

14 = 7a

system%283b%2Api=12a%2Api%2C14=7a%29

Divide the first equation through by 3p.
Divide the second equation through by 7:

system%28b=4a%2C2=a%29

Substitute 2 for "a" in b=4a

b=4(2)
b=8

a+b = 2+8 = 10

Edwin