Chapter 4.1, Problem 45STP

To determine

Find the number of votes received by players for each place.

Answer to Problem 45STP

  $\begin{array}{llll}Player\hfill & 1^{st}placevotes\hfill & 2^{nd}placevotes\hfill & 3^{rd}placevotes\hfill \\ LarryJohnson\hfill & 108\hfill & 130\hfill & 142\hfill \\ KenDorsey\hfill & 122\hfill & 89\hfill & 99\hfill \\ CarsonPalmer\hfill & 242\hfill & 224\hfill & 154\hfill \\ QuentinGriffin\hfill & 1\hfill & 8\hfill & 9\hfill \\ ByronLeftwich\hfill & 22\hfill & 26\hfill & 34\hfill \\ KliffKingsbury\hfill & 6\hfill & 2\hfill & 11\hfill \\ BradBanks\hfill & 199\hfill & 173\hfill & 152\hfill \\ WillisMcGahee\hfill & 101\hfill & 118\hfill & 121\hfill \\ JasonGesser\hfill & 5\hfill & 22\hfill & 15\hfill \\ ChrisBrown\hfill & 5\hfill & 11\hfill & 11\hfill \end{array}$

Explanation of Solution

Given information:

Darren McFadden of Arkansas placed second overall in the Heisman Trophy voting. Players are given $3$ points for every first-place vote, $2$ points for every second-place vote, and $1$ point for every third-place vote. McFadden received $490$ total votes for first, second, and third place, for a total of $878$ points. If he had $4$ more than twice as many second-place votes as third-place votes.

Calculation:

Here, the table contains the votes each player received for first, second, and third place:

  $\begin{array}{llll}Player\hfill & 1^{st}placevotes\hfill & 2^{nd}placevotes\hfill & 3^{rd}placevotes\hfill \\ LarryJohnson\hfill & 108\hfill & 130\hfill & 142\hfill \\ KenDorsey\hfill & 122\hfill & 89\hfill & 99\hfill \\ CarsonPalmer\hfill & 242\hfill & 224\hfill & 154\hfill \\ QuentinGriffin\hfill & 1\hfill & 8\hfill & 9\hfill \\ ByronLeftwich\hfill & 22\hfill & 26\hfill & 34\hfill \\ KliffKingsbury\hfill & 6\hfill & 2\hfill & 11\hfill \\ BradBanks\hfill & 199\hfill & 173\hfill & 152\hfill \\ WillisMcGahee\hfill & 101\hfill & 118\hfill & 121\hfill \\ JasonGesser\hfill & 5\hfill & 22\hfill & 15\hfill \\ ChrisBrown\hfill & 5\hfill & 11\hfill & 11\hfill \end{array}$

Hence, the results are shown in the above table.