Stacking Cups

Stacking Cups - Act 1 from Mr.Stadel on Vimeo.


For this activity we had to figure out many things.

Questions

When does the white cup pass the blue? When are both the blue and white cups equal? What is an equation for this scenario?

What We Did

My group and I tried many methods but we almost immediately found out how to do it. We needed to multiply the amount of cups to the excess amount that would be left on each of the cups, subtracted by one. This is because on the first cup the amount of excess was already included in the height, therefore it was unnecessary to add it in. For the white cup (which has a smaller height) we were given the dimensions 9.2 for the height. The excess amount of 'cup' would be 1.3. For the blue cup the height was 12.1 while the excess amount was .8.

Formula 

The equation that we came up with was R(N-1)+H.

R = Rim
N = Number of cups
H = Height

Conclusion

After we came up with the equation, everything else became simple. We began guessing and checking and we finally came up to a conclusion. The cups will become equal at 7 cups each. The white cup will then pass the blue cup at 8 cups.