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