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PROBLEM OF THE WEEK #11 Solution A car is originally valued at $10,000. MAJ Kevin Cummiskey, being the negotiator that he is, manages to purchase the car for a discount of X %. MAJ Cummiskey and his wife have another child and decide that they need to sell the car. MAJ Scott Seidel has had enough of riding his bike to work in the snow and decides to purchase the car from MAJ Cummiskey at a discount of Y %. MAJ Seidel has his apartment robbed and, unfortunately, let his renter’s insurance lapse. Therefore, he is forced back on the bike again and must take a big hit by selling the car at a discount of (X+Y) %. What is the final sale price of the car? 𝑋 𝑋 1) The first sale, with a discount of X % (or 100), is valued at a price of $10,000 ∗ (1 − 100). 𝑌 2) The second sale is then calculated by multiplying the price in Step 1 by 1 − 100. 3) Similarly, the third and final price is calculated by multiplying the price from Step 2 by 1− 𝑋+𝑌 100 . 𝑋 𝑌 4) Consequently, the final price is 𝑃𝐹 = $10,000 ∗ (1 − 100) ∗ (1 − 100) ∗ (1 − 𝑋+𝑌 100 ). 5) An example: Let X = 7 and Y = 9. The final price would be 7 9 16 𝑃𝐹 = $10,000 ∗ (1 − 100) ∗ (1 − 100) ∗ (1 − 100) = $10,000 ∗ (. 93) ∗ (. 91) ∗ (. 84) = $10,000 ∗ .710892 = $𝟕, 𝟏𝟎𝟖. 𝟗𝟐