Chapter 6.4, Problem 20PPS

To determine

To determine the number of field goals and extra points made by Adam Vinatieri.

Answer to Problem 20PPS

The numbers of field goals are 27

Total extra points earned are 47

Explanation of Solution

Given:

Total number of field goals is 71 and total number of point earned is 125

Calculation:

Let, the numbers of field goals be x and the number of goals after touchdown be y .

Total number of field goals is 71, which means,

  $x+y=-10$

And total number of point earned is 125, which means,

  $3x+y=125$

Let,

  $x+y=\mathrm{71.......}(i)$

  $3x+y=\mathrm{125.......}(ii)$

Now, subtract equation ( i ) from equation ( ii ),

  $\begin{array}{l}\Rightarrow (3x+y)-(x+y)=125-71\\ \Rightarrow 3x+y-x-y=54\\ \Rightarrow 2x=54\\ \Rightarrow x=27\end{array}$

Now, substitute the value of x in equation ( i ),

  $\begin{array}{l}\Rightarrow 27+y=71\\ \Rightarrow y=47\end{array}$

Conclusion:

Therefore, the required numbers of field goals are 27 and total extra points earned are 47.