Hot Dog Eating Contest = Algebra
Big Question: What if the convenience store did not run out of hot dogs for rival competitive eaters
Takeru Kobayashi and Sonya “Black Widow” Thomas to eat?
The Challenge(s)
1. How many hot dogs were on the grill before Kobayashi ordered the first hot dog?
2. How many hot dogs would each person eat in Round 20?
3. How many hot dogs would each person eat in Round n?
4. How many total hot dogs would each person have eaten in Round 20?
5. How many total hot dogs would each person have eaten in Round n?
6. How many hot dogs would Kobayashi have to eat to catch up to Sonya after Round 20 is over?
7. How many hot dogs would Kobayashi have to eat to catch up to Sonya after Round n is over?
In case questions 6 and 7 are unclear, what I mean is that Kobayashi starts to fall behind
Sonya at the end of the first round because she orders one more than him. This continues
and he falls farther behind her. So, how many hot dogs would he have to eat to catch up to her?
QR code to watch the video.
Counting hot dogs?!?
I have saved a couple of screen shots of the hot dogs. Go to our
class website and search for it under the Math tab.
On the screen shots you can clearly see four columns with at least
eight hot dogs per column. For the sake of this problem, I am
going to pretend that they each have exactly nine hot dogs in
each of the four columns. The screen shots will help make this
clearer:
You’re welcome.
Consider This
Kobayashi, speaks in Japanese and it may not be clear at first that his one finger is asking for one hot
dog. Once, Sonya says that she wants two hot dogs, the meaning behind him holding up three fingers
should be clear.
I define each “round” as each of them getting to order hot dog(s). So in Round 1, Kobayashi eats one
hot dog and Sonya eats two hot dogs. In Round 2, Kobayashi eats three additional hot dogs and Sonya
eats four additional hot dogs. This continues until Kobayashi tries to order nine hot dogs to begin
Round 5 and finds that the store has run out.
Question(s) To Ask Yourselves While Solving This:

What is a guess that is too low?

What is a guess that is too high?

What is your best guess?

How many hot dogs did each person order each round?

What pattern do you see?

How can we record this information?

How many total hot dogs did each person eat in the first four rounds?
Success Criteria:

Neatly answer each question posted on a separate piece of lined paper after you have done
all your rough work.

Develop a table to record all results. This table should be prepared very neatly (can draw or
create using technology) and be handed in.

Develop a formula/algorithm to solve the problem. This formula should be included in your
conclusion.
ALL WORK WILL BE HANDED IN. PLEASE HAND IN YOUR WORK STAPLED IN THE FOLLOWING
ORDER:
1. CONCLUSION SHEET
2. ANSWERS
3. TABLE
4. ROUGH WORK
**You may choose to do this alone. That is fine. But once you have made that decision there is no going back.
**Working with one partner only. No groups of 3. You may not switch partners or decide to work alone once
you have made your decision.
Name:_____________________________________________
Math partner’s name:______________________________
*staple all work (table, answers, rough work ) to this sheet and hand in. This sheet should be filled out neatly.
What problem are you trying to figure out?
What do you already know from the problem?
What do you need to know to solve the problem?
What is your conclusion? How did you reach your conclusion?