Mrs. Hillestad has planned a dinner for 15 people this Thanksgiving. She bought 22.5 lbs of turkey, plus potatoes, cranberry salad, rolls and all of the traditional holiday food. Unfortunately, her daughter forgot to tell her that she was bringing three of her friends. If Mrs. Hillestad wants to feed each person the same amount of turkey that she had originally planned, how much additional turkey must she purchase to accommodate these additional guests? Express your answer as a decimal to the nearest tenth.
First, we need to determine how much turkey Mrs. Hillestad wanted to give each person. We divide 22.5 lbs ÷ 15 people and see that she planned to serve each person 1.5 lbs of turkey. Now we multiply the per person amount of turkey by the number of additional people that showed up. It follows, then, that Mrs. Hillestad will need to purchase an additional 1.5 × 3 = 4.5 lbs of turkey.
Mrs. Hillestad realizes that she doesn’t have the time to go to the store AND make the extra turkey. So, she decides not to purchase additional turkey. Since the 22.5 lbs of turkey that Mrs. Hillestad already purchased must now be equally divided among 18 people, by what percent is each person’s intended serving of turkey reduced?
In the previous problem, we determined that the intended serving size was 1.5 lbs per person. Now we need to determine the new serving size when the 22.5 lbs of turkey is equally divided among 18 people. Dividing, we see that each person will get 22.5 lbs ÷ 18 people = 1.25 lbs of turkey. Next, we’ll determine the actual amount of turkey that each person’s serving was reduced by. Subtracting, we see that each person’s serving was reduced by 1.5 – 1.25 = 0.25 lbs of turkey. Finally, we divide the amount by which each person’s serving was reduced by the amount Mrs. Hillestad originally intended to serve each person and then multiply by 100 to find the percent of decrease. Doing so, we see that each person’s intended serving of turkey was reduced by (0.25 ÷ 1.5) × 100 = 16.66%.
At dinner time the eight adults sit at a large round table, and the ten kids sit at the “kiddie” table. Mr. And Mrs. Hillestad will sit next to each other in designated seats, as shown, but the rest of the adults can be seated randomly around the table. How many different seating arrangements are possible?
Since Mr. and Mrs. H. will sit next to each other in designated seats, we are really just concerned about the other six seats. To figure this out we will use a factorial (for the first seat there are 6 potential people who could be seated, for the second seat there are 5 people left to be seated, etc.). Therefore, there are 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720 possible seating arrangements.
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