April 4, 2011
Introduction to Integrated Math
A Sticky Gum Problem
This POW didn’t have a specific problem but it does have a few problems with gumballs. Well there were 3 questions but I had added 3 questions of my own. But first I started with answering the questions. Question 1: Mrs. Hernandez comes across a gumball machine one day when she was out with her twins. Of course, the twins each wanted a gumball. They also insist on having the same color. They don’t care what color the gumballs are, as long as they’re both the same. Ms. Hernandez can see that there are only white and red gumballs in the machine. The gumballs cost a penny each and there is no way to tell which color is going to come out next. Mrs. Hernandez decides to keep putting in pennies until she gets two gumballs of the same color. Problem 1: Why is three cents the most Mrs. Hernandez might have to spend? Question 2: The next day Mrs. Hernandez and her twins pass another gumball machine. This one has three colors: red, white and blue. Problem 2: What is the most Mrs. Hernandez might have to spend at this machine to get matching gumball? Question 3: Mr. Hodges and his triplets pass the three-color gumball machine. Of course, his children insist that they all want the same color gumballs. Problem 3: What is the most Mr. Hodges might have to spend?
Well now enclosed is my work. I drew 3 diagrams for the gumball spending. The basic problem throughout all these questions is that all of the kids are in love with gumballs and want to be the same. Luckily I have found the answer to them. I’m going to answer them and then if you would like to know how I got my answer just turn the page and you will see all of my work. Problem 1: Why is three cents the most Mrs. Hernandez might have to spend? Well since she has three cents there is a good chance that she will get a match because in the machine, there are 2 colors and she...