Puzzlers

HERE ARE A COUPLE OF PROBLEMS I MADE UP TO CHALLENGE STUDENTS.

MR. HOUDEK’S KENNEL

Problem #1) Mr. Houdek wants to build a kennel for his dog. He has 36 feet of chain link fencing and would like to make the kennel as large as possible. What shape and dimensions should he build the kennel to get the largest area for his dog? What would the area be? Show work and/or give an explanation to justify your answer.

Problem #2) Assuming for the above problem, the kennel had to be in the shape of a rectangle, what dimensions would give the largest area? What would the area be? Show work and/or give an explanation to justify your answer.

Problem #3) Mr. Houdek decides to build his rectangular kennel next to his 24 foot long garage, so he only needs fencing on three sides. What should the dimensions of the rectangle be to get the largest area? What would the area be? Show work and/or give an explanation to justify your answer.

Mr. Houdek’s Tomatoes

Mr. Houdek has a garden that on August 20th had 400 tomatoes in it. That night the deer discovered his garden and ate or trampled 1/5 of his tomatoes. On August 21st , Mr. Houdek picked 5 tomatoes that the deer didn’t get. The next night and day the same thing happened again, the deer ate 1/5 of what was left and Mr. Houdek picked 5. This pattern kept on in the same manner until all the tomatoes were gone. When were all the tomatoes gone, how many did Mr. Houdek get and how many did the deer get. Answer this questions as best you can. Support your answer with whatever you can.