 In this video, we provide the solution to question number 15 for practice exam 2 for math 1030. In which case we have three friends here, Annabelle and Claire, and they have to divide up four pieces of furniture they shared using the method of sealed bids. Their bids are listed here on the table below, and so we have to decide which of the four assets will be given to each of the three players and then how will their, how's the money managed by the end of this problem here. So let's first look at the bids. So for a dresser, Anna bid $150, Belle bid $300, Chloe bid $275. So Belle had the highest bid, and Belle will be the one who receives the dresser, or maybe it's just a dress, I don't actually know, said furniture. Next, a desk, Anna bid $180, Belle did $150, Chloe did $165, $180 is the highest bid, so Anna will be receiving the desk, like so. For a vanity, Anna bid $170, Belle bid $200, Chloe bid $260. So we see that is the highest price, the highest bid there. So the vanity is going to go to Chloe. And then lastly for a tapestry, Anna bid $400, Chloe bid $250, and Chloe bid, so Belle did $250 and Chloe did $500. So the tapestry is going to go to Chloe as well. So we see which of the assets will go to which of the people. So we didn't have to consider how the money is going to go to this state and everything. So we have to add together, how much does Anna think is a fair share? So if you take $150 plus $180 plus $170 plus $400, that gives you a total of $900, for which as there's three people there, if you divide that by three, that then says that Anna sees a fair share as $300. What about Belle? Belle, she bid $300 for the dresser, $250 for the vanity, $250 for the desk, and then $250 for the tapestry. That gives Belle also a total of $900, which if you divide that by three, that's where you get $300. And then finally, if you take Chloe there, she bid $275 for the dresser, $165 for the desk, $260 for the vanity, and then $500 for the tapestry. If you add that all up, that then gives a total of $1,200, for which if you divide by three, you end up with $400, being what Chloe sees as a fair share. Okay. So then we have to calculate what do they owe to the estate? Well, since Anna is going to get the desk, she needs to pay $180 to the estate. Belle, she bid and won the dresser, which would be $300. So she's going to pay $300 to the estate. Chloe bid and won the vanity and the tapestry. So $260 plus $500, that is a total of $760 that she should owe to the estate. So that's how much they have to pay those things. So Anna, she believes she's owed $300. She needs to pay $180. If you take the difference, that gives you $120. With Belle, if we take the difference, she's owed $300. She pays $300. So the difference would be zero. And for Chloe's situation, she is owed $400, but she owes $760. So that difference is going to give you negative $360 there. Okay. If you add those together, $120 plus zero minus 360, that's going to give us a surplus of $240 to the estate. So if we take all that and divide it by three, all right, so that gives $80 to everyone. So we're going to add $80 to each and every one of these. So to Anna, she's owed $120, but there's a surplus of $80 for her. So that adds up and gives her $200. So what she then would get is she would get $200 from the estate and the desk. As for Belle, her difference was zero. We add to it $80. So she's going to get $80 from the estate and she gets the dresser. That gives her a fair share. Now finally, for Chloe here, she owes the estate $360. If we add $80 to that, then in the end, she pays to the estate $280. She will get the vanity and the tapestry. And notice, of course, so this is a negative there. So she pays to the estate $280. That $280 we've broken up into $280 for Anna and Belle. And so the sum of the last line should be zero. And that's how the four assets will be distributed amongst the three players and the money they will also get. And everyone will get a fair share.