The Race to Eat 100 Plates

by Laura Overdeck

The holiday eating season is just getting started, which may be why our friend Charlize C. asked, how long would it take to eat 100 plates of food? Well, that depends on both the food and the person eating it. Competitive speed-eaters can eat 13 grilled cheese sandwiches in just 1 minute. *IF* they could eat nonstop at that pace, that speed-eater could eat 100 plates of grilled cheese in fewer than 8 minutes!

Wee ones: If you ate 2 plates of food on Thanksgiving and 1 plate of leftovers the next day, how many plates of Thanksgiving food did you have?

Little kids: If you eat a plate of pancakes, then a plate of pasta, then a plate of pancakes, then a plate of pasta…which food is on the 9th plate? Bonus: If you eat 10 plates of pancakes every day for 1 week, can you eat 100 plates of pancakes in those 7 days?

Big kids: If you can eat 12 burgers in 3 minutes and 2 pizzas in 1 minute, which do you eat faster, a burger or a pizza? Bonus: How many more burgers than pizzas can you eat in 15 minutes?   

The sky’s the limit: If a speed-eater eats twice as many hamburgers as pizzas, and twice as many salads as hamburgers, and eats 49 plates in total…how many plates of each food does she eat?

Answers: 

Wee ones: 3 plates of Thanksgiving food.

Little kids: Pancakes, since it’s on the 1st, 3rd, and every following odd-numbered plate. Bonus: Not quite – you’ll eat only 70 plates.   

Big kids: You eat burgers more quickly: dividing 12 burgers by 3 minutes comes to 4 burgers per minute, compared to 2 pizzas in a minute. Bonus: 30 more burgers than pizzas. 4 burgers per minute comes to 60 burgers, while 2 pizzas per minute comes to “only” 30 pizzas.

The sky’s the limit: 7 plates of pizza, 14 plates of hamburgers, and 28 plates of salad. Each pizza comes with 2 burgers and 4 salads (2 salads per burger), which makes a set of 7 plates, and there are 7 sets of 7 plates in 49 plates. That gives us 7 pizzas, then twice as many burgers and so on.

You can see this in action if you solve this using algebra. Since the pizza (p), hamburger (h) and salad (s) plates add up to 49, then:

p + h + s = 49

And since there are twice as many hamburger as pizza plates: h = 2p

And twice as many salad plates as hamburger plates: s = 2h = 4p

Substituting those values back into the original formula:

p + h + s = p + 2p + 4p = 49

7p = 49

P = 7 = the number of pizzas. From there you use 2p and 4p to figure out the other foods!

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