Question

Dear Mitch,

Can you please give the answer to the Thanksgiving problem about the stuffing and the lady who got one free pound for every five she bought. And can you explain it? Because at the end you say"Hint: think of it as a ratio question", but I didn't get what you meant by that.

Thanks a lot,

Todd Seiden,

Middle School Math Student

Just outside New Orleans, LA

Answer

Dear Todd,

Sure. First, in case anyone missed it the question was as follows:

"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....)"

Okay, I don't know if you ever read it, but a while back I presented ratios and how I think one can think of them so that they become immediately clear. It's easy to find in the archived q&a's, but here is a quick version of my concept:

Think of ratio questions as questions about shrink-wrapped packages.If you are not sure what the term 'shrink-wrapped' means, it refers to those packages in stores of more than one item that are not sold separately and cannot be separated because they have been sealed together using a plastic that has been heated closed around them. (The packaging could also contain cardboard, wire, etc. but the idea is the same: if you want one of the items you have to buy all of them packaged together whether you need them or not.) For example, batteries often come in shrink-wrapped packages, so that it is easy to purchase a package of two or four or eight, but not always easy to find one battery by itself (unless it is a rather large battery, particularly one for an automobile). Or you may wish to purchase one tennis ball but find that they only come in packs of three.

Okay, ratios are like that: groups of items that always come in a certain kind of a group. In this problem, the groups (or shrink-wrapped packages") are formed like this: (5 pounds of stuffing + one pound of FREE stuffing)

So you cannot separate that group to get the one free pound by itself or rearrange it with other groups to make it half regular pounds and half free pounds. They are grouped together in six pound 'packs'.

The problem states that the woman left the store with thirty pounds. That means that she must have taken 5 of these six-pound 'packs'. Stacked, they would look (sort of) like this:

(5 pounds + 1 Free) = 6 pounds

(5 pounds + 1 Free) = 6 pounds

(5 pounds + 1 Free) = 6 pounds

(5 pounds + 1 Free) = 6 pounds

(5 pounds + 1 Free) = 6 pounds

And since 1 pound in each pack was free, altogether she received 5 pounds free and paid for 25 of the thirty pounds.The problem states that the total amount she spent was $75.00.

To get the price per pound you divide the total cost by the number of pounds she actually paid for.So you have $75.00 divided by 25 pounds.=

75/25 = 3

She paid $3.00 for each pound she bought. Answer choice B.

Hope this helps,

Mitch