Aanen Kulseth, Marjorie Borer Seabloom, and Sylas Kolb Simplify: Jenny and Carly go shopping together. Jenny is buying two pairs of shoes, one for $110 and another pair for $100. Carly is buying a pair costing $160. The store is having a buy two get one free, the free shoe will be the cheapest one. Jenny and Carly must now decide how to fairly divide the discount between the two of them. Our definition of fairness for Jenny and Carly is not taking advantage of each other. This means that they are doing what they deem is right, and they are not trying to trick or outsmart the other person in order to pay less. Assumptions: 1. The discount in this situation will always be $100. 2. Jenny will always get two shoes and Carly will always get one. 3. They won’t steal the shoes. 4. They are friends and will try and split it fairly, nor will they try to trick each other. 5. Both friends have enough money to pay for all of the shoes if necessary. Variables: t = total cost of shoes per person d = discount a = amount paid p = # of people the discount is split over Solve: Instead of splitting the final total, they would split the $100 discount evenly. Essentially, they are both getting a $50 dollar discount. Paying this way would lead to Jenny’s original bill of $210 dropping down to $160. This would also drop Carly’s bill from 160 down to $110. t = total cost of shoes for a specific person d = discount a = amount paid p = # of people the discount is split over t - (d/p) = a Extend: Aanen’s Extend: My version of the problem would be similar in the nature and background of the problem. The shoes prices are now different and there are more shoes. The cheapest one will always be the one discounted. They are shopping in California and have to pay a sales tax of 7.25%. Sales tax is added after the discount is calculated. And most importantly, Carly has a premium member card which entitles her to a 20% bigger discount whenever there is currently a deal. Carly decided to not share this discount because she has to pay for the membership, but that price is not included here. The shoe prices are: $239.99(shoe 1) $134.99(shoe 2) $159.99(shoe 3) $79.99(shoe 4) Totaling $614.96 Jenny is purchasing shoes 2 and 3. Carly is purchasing shoes 1 and 4. For starters, they round shoe 4’s price to $80 while calculating and Carly offers to pay the extra cent later. Carly’s discount is $56 while Jenny’s is only $40. This is due to Carly’s discount membership card. Equation for Carly’s discount 80/2 + (80 x 0.2) = 56 Equation for Jenny’s discount 80/2 = 40 Jenny Carly $134.99 $239.99 +$159.99 +$79.99 -$40 (discount) -$56 (discount + member card) ——— ——— $254.98 $263.98 +$18.49(sales tax) +$19.14(sales tax) ——— ——— $273.47 $283.12 +$0.1 Sales tax was calculated by multiplying the total after applying the discount, for each person. Carly decides to throw in the extra cent in order to make it work. This would leave their final totals with Jenny paying $273.47, and Carly paying $283.13. Sylas’ Extend: In my version of the problem they decide to split the discount based on what percentage of the total cost of all three pairs of shoes without the discount. The total comes out to $370, Jenny’s total without a discount is $210 and Carly’s is $160. From there we can figure out what percentage of the total cost they each make up. Jenny’s Percentage $210 / $370 = 0.56756 Jenny has 56.76% of the total cost. For Carly we can assume that her percentage of the total cost is 43.24% by subtracting 56.76 from 100. From here we can divide the $100 discount between them using the percentages as our guideline. Jenny gets a $56.76 discount, while Carly gets a $43.24 discount. Jenny $210.00 -$56.76 ———— $153.24 Carly $160.00 -$43.24 ———— $116.76 Marjorie’s Extend: For my extend instead of having a flat discount, it will be a buy 5 shoes, get 1 free. The free one will be the cheapest out of the 6 pairs of shoes. There will also be 4 people who are friends, Jenny who gets 1 pair for 220 and 1 for 100, Carly who gets 1 pair for 200, Chris P. Bacon who gets 1 pair for 150 and then Custard who just gets 1 pair for 125. Because they are friends they decide to just split the price off of the 1 pair of shoes between them evenly. This would mean that each person gets 25 dollars off. First you would divide 100/4=25 Next you would add up everyone’s prices Jenny 210 +100 ——— 310 Carly 200 Custard 125 Chris P. Bacon 150 ———200 ——— 125 ————150 Next you will subtract their discount to get their final price Jenny 210 -25 ——— Carly 200 -25 ———- Custard 125 -25 ——— Chris P. Bacon 150 -25 ————- 185 175 100 125
