Farmer Hank and his Pigs

Farmer Hank

The first day of Math 257 class, our instructor gave us a warm up problem.  I believe the intention behind this was to get our critical thinking going and prepare us for the weeks ahead.  The warm up problem was about a farmer named Hank who had fewer than 100 pigs on his farm.  If he groups the pigs five to a pen, there are always three pigs left over.  If he groups the pigs seven to a pen, there is always one pig left over.  However, if he groups the pigs three to a pen, there are no pigs left over.  What is the greatest number of pigs that Farmer Hank could have on his farm?

I approached this problem by highlighting all the givens first.  Then, I started at the highest number if grouped into five and three pigs were left over which was 98 pigs.  However, 98 pigs didn't equal out with seven and one left over.  So, I moved down to 93, 88, 83 pigs and none of these numbers equal out to seven and one left over.  Once, I reached 78 pigs, it worked out!  The number 78 came out to: 15 groups of 5's with 3 pigs left over, 11 groups of 7's with 1 pig left over, and 26 groups of 3's with no pigs left over.  Therefore, the greatest number of pigs that Farmer Hank could have on his farm that was fewer than 100 pigs was 78 pigs.  

We had a similar problem in my Math 256 class about, A Farmer and her Broken Eggs.

Sources:

http://clipart.coolclips.com/480/v

Tachine-Benally, Miranda. Farmer Hank Warm Up. 03 Oct. 2016. Classroom Worksheet. Mesa Community College. Mesa.