# 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
2*N*, 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

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

3*N* + 3 = 4*N* - 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 7*M* 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

7*M* = 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**!

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