(10 point question): If my dad (Rev. Rodney L. Swisher) was alive today, he would be watching with his two sons today’s Cowboys-Redskins football game at 3:30 PM CST as we would be helping ourselves to another helping of a delicious Thanksgiving dinner. Suppose that my dad was around to place a wager between him and his sons. The wager would be based on how well the two starting quarterbacks (most likely Dak Prescott for the Cowboys and the new starter Colt McCoy for the Redskins) perform in this football game. Joel (my brother) and I would take the Redskins quarterback; Dad would take the Cowboys quarterback. Money will be determined from the following point scheme:
+ 1 point for every 25 yards passed
+ 1 point for every 10 yards rushed
– 3 points for every interception thrown by the quarterback
– 2 points for every time the quarterback is sacked
+ 4 points for every passing touchdown
+ 6 points for every rushing touchdown
+ 2 points for a passing touchdown of at least 40 yards
+ 3 points for a passing touchdown of at least 50 yards
+ 5 points for ending the game with at least 300 passing yards

For example, if McCoy threw a 62-yard touchdown pass, this would amount to 11.48 points for this one play
and the Swisher brothers would have earned $11.48 total.

Now, suppose that Dad’s quarterback will pass for a total of 256 yards, rush for a total of 31 yards, throw 1
interception, get sacked twice, rush in for 1 touchdown, and have 2 passing touchdowns in this game (1 of these
touchdowns went for 44 yards and the other went for 20 yards). Our quarterback will pass for a total of 315
yards, rush for a total of 16 yards, throw 2 interceptions, get sacked once, and have 4 passing touchdowns (one
went for 6 yards, another went 34 yards, and the other went for 55 yards). The winner of the wager will receive
from the loser the difference in the points earned between these quarterbacks in dollars and cents. (If Joel & I
were to win, we would split the winnings.) Based on the given information, who would win this wager and how
much money would the winner receive?

Please show all work

Respuesta :

First of all, as a football fan, 50 passing yards crossing out a sack doesn't make sense.


Formatting this a bit better, we have:

Passing Yards

Dak: 256        Colt: 315 (+300 bonus)

Rushing Yards

Dak: 31            Colt: 16

INTs

Dak: 1           Colt: 2

Sacks

Dak: 2        Colt: 1

Passing TDs (0-40 yards)

Dak: 1         Colt: 2 (you only listed 3 yardages for Colt's touchdowns, yet said he had 4, so you'll need to edit the final answer. In addition, I don't know if passing TDs from 50+ yards are counted as a passing TD from 40+ yards, 50+ yards as well, so I'll assume that it doesn't)

Passing TDs (40-50 yards)

Dak: 1      Colt: 0

Passing TDs (50+ yards)

Dak:0     Colt: 1


To figure this out, instead of going and calculating both scores separately, what I will do is subtract Dak's count from Colt's count for each stat, and that difference will therefore be how much the brothers won from that stat. If it's negative, the brothers lose that much money, and I'll add the numbers at the end. Note that the 300 yard bonus is not counted in this, so I'll add 5 to Colt's number at the end. To figure out the rushing/passing yards, we can simply divide the numbers by 25/10 because it's for every amount of yardage, you get a point. For all others, we simply multiply the amount by the amount per sack, INT, rushing touchdown, etc.. Without further ado, here's our end number equation:

5+(315-256)/25+(16-31)/10+(2-1)*(-3)+(1-2)*(-2)+4*(4-2)+2*(0-1)+3*(1-0)=13.86


Feel free to ask further questions, and Happy Thanksgiving!