Value of a+b+c

There are positive integers a,b, and c that satisfy this system of two equations:
What is the value of a+b+c?
Source: NCTM Mathematics Teacher, November 2006

Multiply the first equation by \textrm{-}1, the second equation by 2 and add them
43 =1\times 43 because 43 is a prime number.
a+b+c cannot equal 1 because a,b,c are positive integers.
a+b+c=43 and a+b-c=1.

Answer: 43


About mvtrinh

Retired high school math teacher.
This entry was posted in Problem solving and tagged , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s