From the past two weeks, November 13 to November 24, we chose the problem from Friday November 24 (that you can find here):
All stores are offering amazing deals for Black Friday. Dan wants to buy a huge TV, a Home Theater system, and a sofa at a store. The regular price for the TV is $\$1100$; the regular price for the Home Theater system is $\$1600$; and the regular price for the sofa is $\$450$. This store is offering a deal where they will charge no tax and will also give back a gift card with $25\%$ of the value of the purchase that can be used to buy more items. Dan will buy each item separately, so that after buying each item he will get some money in the gift card that he can use for following items to avoid paying full price. Depending on the order in which he buys each item he may spend a different amount of cash, so he needs to decide what is the best way to purchase the items to spend the least amount of money. How many dollars would he pay in cash to the store using the best possible method?
27% of the students who tried the problem got it right on their first attempt.
This problem is describing a situation to which you or your parents can relate. I'm sure every year you hear about the amazing deals all stores offer for Black Friday, which are so good that some people even camp outside stores to make sure they are the firsts to come in and get the best deals! Have you ever seen a deal like this? One should pay attention to the deals to get the best price!
In deals like the one described in the problem it is always better to start by paying for the most expensive item first, then continue with the second most expensive, and so on. This allows the gift card to have as much money as possible each time, thus spending less out of pocket money.
A popular answer was $\$2750$. This is the amount you would pay if you paid first for the most expensive item (the Home Theater system) and then used the $1600\times.25 = 400$ dollar gift card to pay for the other two items together. However, we can still buy the other two items separately and pay even less money!
Another popular answer was $\$2362.50$. This corresponds to the price one would pay if all three articles had a $25\%$ discount, however, this is not the case. Remember to always make sure to read all the problem thoroughly to make sure you understand the context of the problem and what is it asking.
Make sure to share your thoughts and questions below!