Gumball Problem
For this problem we started out with 3 simple questions:
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Ms. Hernandez and her twins come across a gumball machine with 2 colors in it, red and white. Each gumball costs 1 penny and her twins want the same color gumball. In the worst case scenario what is the most she will need to spend?
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The next day Ms. Hernandez and her twins come across another gumball machine. The gumballs still cost the same and her twins still want the same color, but this time there is 3 different gumball colors, red, white and blue. In the worst case scenario what is the most she will need to spend?
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The next day Mr. Hodges comes along with his triplets to the gumball machine that has 3 colors. His triplets all want the same color. In the worst case scenario what is the most he will need to spend?
After solving each of these problems we were told to change one of the variables, Kids (k) or Number of gumball colors (c). Pennys (p) always remains at 1 cent. We then changed the problem around until we found an equation that worked.
For this problem I started out by solving the first three problems by drawing out circles to represent the gumballs. Once I figured out these three problems I found it easier to do the problem in my head. Once I had the first three solved I made a chart where I changed only the number of colors and left the kids the same, for about 4 equations. Then I changed only the number of kids and left the number of colors the same.
This allowed me to be able to see a pattern and create my equation.
Solution for the first three starting problems:
Solution for the rest of the problem:
Throughout this problem I learned a lot about how to set up a problem like this and how to solve it better in my head. For this problem I think I deserve a 10/10. I did a lot of work on this problem and organized it so it was easier to read. For this problem a few habit of a mathematician that used were:
Look for patterns: I need this to solve the problem because I was supposed to find an equation that would solve the problem and without a pattern there is no way to do find one.
Stay organized: I need this to see the patterns throughout my chart because if it was not organized I wouldn’t be able to see the patterns throughout my data.
Visualiza: I need this in the beginning of this problem so that I was able to solve the problem by looking at the different colors of gumballs.