Question

Dear Mitch,

A few days ago you posted a question from a middle school math teacher who wanted some Thanksgiving math questions, and in your answer you gave a pretty interesting one. Then you said you'd post an answer or hint or something in the next day or two. But I've been checking. I haven't seen any hints or answers. Where should I be looking?

Also, either the day before that letter or the day after, you posted another letter basically asking for the same thing. Again, I liked the Thanksgiving math questions you gave for middle school students, but I couldn't find the hints or answers for those either. Please help.

Thank you,

Nicki C.

(Student-Teacher Completing Her Requirements For Middle School Certification,

Portland, OR)

Answer

Dear Nicki,

Sorry you've been hanging on for longer than we planned!

What happened is that we received such an unexpectedly large response to those last two posted letters, most of which included the incorrect answer choice that shows how tricky one of the questions was, that we realized it would be a better idea to hold off another couple of days before giving the answers. (Somehow, we have found that once an answer is posted, the questions become less exciting for people to try on their own, even teachers!)

So thank you for waiting. Beginning today, we will answer and explain one Thanksgiving problem each day. So, to review:

The November 1^{st} letter presented two Math problems:

- For Thanksgiving, a neighborhood grocery store in Clayton, Missouri was giving customers one free pound of stuffing with every 5 pounds the customer buys. Mrs. McFergass Donahaus Rebitz McIntire III entered the store. She was well-known in the area for one thing : she enjoyed her stuffing. Oh, she'd invite you to dinner if you were in need of a place to go but don't touch her stuffing – at least not if you'd like to ever get another invitation...

So, that day when Mrs. McFergass Donahaus Rebitz McIntire III entered the store she bought only

stuffing and left the store with 30 pounds of the stuff (stuffing). If she spent $75.00, how many dollars does each pound of stuffing sell for?

(A) 2

(B) 3

(C) 6

(D) 9

(E) 20

(HINT: Think of this as a ratio question....)

2. In the 8^{th} grade social studies community service class, the students were required to either cook a turkey or a make a soup; the food when then be distributed to local families who otherwise would have very little for the holiday. If a student wished to, he or she could make *both* a turkey *and* a soup, but if a student didn't make either then he/she would not be released from the darkened classroom, alone, until the holiday weekend was over.

23 students each made a soup, 27 students each made a turkey. If there were 41 students in all, how many students made a soup but not a turkey?

This problem, #2, which involves the soup-makers and the turkey-makers is the one we will answer now. Then we will answer #1 tomorrow and the third question on the following day. Hope the suspense is not too much!

This one, #1, is a very popular type of question that seems tricky at first but with a little practice becomes very straightforward.

The first thing you probably notice is that when you add up the number of students who are in the turkey-making group with the number of students who are in the soup-making group you end up with a number that is larger than the total number of students altogether. That seems to confuse some people. All it means is that some of the students are being counted twice because they are in both groups (recall, the problem states that a student may be in both groups, but cannot be in neither).

The easiest way to do such a question is to draw a Venn Diagram. Remember those? Something like this:

Next, you label one of the loops with a T (for turkey-makers).

Label the other loop with an S (for soup-makers).

Next, you figure out how many students are being double-counted. That you get by adding up the two groups and seeing how many more 'counts' you have than there would be if each students was only counted once (the difference).

So, 23 students are in the soup-maker group, and 27 are in the turkey-maker group.

23 + 27 = 50.

The problem states that there were 41 students in all.

Therefore, since 50 – 41 = 9, it means that nine students were being counted twice.

In a Venn diagram, the number of students who are in both categories gets written in the intersecting portion.

So you have 9 in the middle.

Then, you subtract that number from the total number of turkey-makers, and you get 27- 9 = 18.

You write that number in the loop labeled T that is not intersecting, so students are not double-counted if they are not in both groups. T

You do the same thing with the number of students in the soup-group. 23 - 9 = 14.

And you write 14 in the loop labeled with a n S, but not the intersecting part.

At this point it is easy to check if you have arrived at all the correct numbers, but I'll leave that you to you to figure out! (For now).

Next you reread the question to find out exactly what is being asked of you. Here they are asking how many students are making soup but not a turkey.

SO: you look at the part of your Venn diagram that shows how many are in the 'S' loop but NOT the intersecting portion. And that part says: 14.

So the answer is 14 students are making soup but not turkey.

Hope this helps,

Mitch