Internet Math Challenge

Solution to the puzzle for 5 December 2003

The number of sandwiches eaten on Friday is 21. Here's how to get that answer:

The first thing we need to do is figure out how many people were involved. Let's let N represent the number of people at Thanksgiving dinner on Thursday. Then, the number of orange rolls eaten on Thursday is 2N, and the number eaten on Friday is N-4 (remember that 4 people left on Thursday night). Since there were 7 orange rolls left Friday night, a total of

2N + (N-4) + 7 = 3N + 3

orange rolls were baked.

There were N pie slices eaten Thursday and 3(N-4) pie slices eaten Friday. There were 4 slices (two-thirds of a pie) remaining on Friday night. So, the total number of pie slices baked must have been

N + 3(N-4) + 4 = 4N - 8.

We can now figure out how many people were at Thanksgiving dinner! There were originally equal numbers of orange rolls and pie slices, so:

3N + 3 = 4N - 8

which leads easily to the value N = 11.

So, there were 11 people at the house on Thursday, 7 on Friday, and (since 2 more people leave Friday night) 5 on Saturday. Now we're getting somewhere! Let's let M be the number of turkey sandwiches eaten by each person on Friday. Then a total of 7M sandwiches are eaten Friday, and 5(M-1) are eaten on Saturday. Since Friday's total is 11 greater than Saturday's, we have the equation

7M = 5(M-1) + 11

which leads to the value M = 3.

Now we have the answer: 7 people ate 3 sandwiches each on Friday -- a total of 21 sandwiches!

Thanks to these sponsors for their generous support of the IMC!