Thanksgiving Day Math

This is a long word problem that my students and I developed when year while working on feasible region problems. I hope you enjoy it as much as we do.

Mr. Brabec was getting ready for Thanksgiving and needed to figure out how many potatoes to buy for his guests. He jumped on his bike and rode over to the supermarket because he knew the parking would be a mess. Because he was on his bike, he knew that he could only carry home a maximum of 15 pounds of groceries. In the produce section he found that the sweet potatoes weighed ⅓ of a pound each and that the only white potatoes left were 5 pound bags which each contained 12 potatoes. Before buying any potatoes, Mr. Brabec thought he better check to see if the store had any butter. When he made it over to the butter aisle, he found that there were only 3 pounds left so he quickly grabbed them both because Thanksgiving wouldn’t be the same without butter. Besides, his recipe for sweet potatoes called for 1 stick of butter for each 2.5 sweet potatoes and 1 stick for each 4 white potatoes and he still needed 1 stick to make the pie crust for his apple pie.

As he wandered back through the crowds at the grocery store, Mr Brabec thought about all the other things that he was going to make on Thursday. He only has the one oven at the house which had a total of six square feet of rack space. Baking the pie and the turkey could be done in advance but the sweet potatoes and mashed potatoes would need to share space with the green bean casserole. The casserole pan is 9” x 13” and can easily fit with other things but sweet potatoes take up a lot of space because of all the marshmallows on top. They require two square feet for every ten sweet potatoes. The mashed potatoes would need to stay warm before dinner so they will be in the oven too. They can be piled high in a baking dish and will only take up one square foot of oven space for every ten potatoes.

What about other ingredients? Mr. Brabec had plenty of marshmallows at home because his girls love them on their hot cocoa. He also had plenty of milk so no need to get any more. Salt was the big question. The recipe for sweet potatoes called for ½ teaspoon of salt for every 5 sweet potatoes he used. The mashed potato recipe was a little more savory and required ½ teaspoon for every 3 potatoes, but how much salt did he have at home? He had brined the turkey that morning and recalled that there was ¼ cup of salt left in the container, but was that enough? Rather than trying to brave another expedition across the busy store he decided that it would have to be enough.

As he weaved his way through the crowds, Mr. B. thought about how much time he had to get things ready for the big meal. Peeling potatoes was something he dreaded because it took so much time and it made his hands all starchy. He decided that we would keep his potato peeling time to less than 20 minutes this year since last year he got a blister on his thumb after peeling for a half hour. Mr. Brabec can peel a sweet potato in 30 seconds and a white potato in 25 seconds so he should have plenty of time.

As he got to the produce aisle once again, Mr. B thought about the guest that would be at his dinner party. There were going to be twenty people there but not everyone liked everything. Cousin Charles and his family of four grew up always eating sweet potatoes at their home in Atlanta and they would not eat any mashed potatoes. Mr. B and his wife and two kids would want both kinds of potatoes. The Smiths (six in total) were from Idaho and they believed that the only “real” potatoes were mashed potatoes and they would never be caught eating any sweet potatoes at Thanksgiving. Mr. Brabec’s in-laws were a mixed bunch. Half of their family of six would eat only mashed potatoes and the other half would eat only sweet potatoes.

So many things to consider. As he stood there in front of the potato bins Mr. Brabec wondered, “How many potatoes of each kind should I buy so that everyone can have the greatest number of each type of potato that they want for the holiday feast?”