Chapter 8.2, Problem 74SR

To determine

To calculate: The expression for the total time for the trip.

Answer to Problem 74SR

The required number of 2 point field goal is 514 and 3 point field is 3.

Explanation of Solution

Given information:

Tim Duncan score total 1342 points.

Point scored by free throw is 305.

Total no of field goal=517

Calculation:

Given that Tim Duncan score total 1342 points.

Now, find the number of goals. Subtract point scored by free throw from total score.

Number of field goals $\begin{array}{l}=1342-305\\ =1037\end{array}$

Let 2 point goal is $x$ and 3 point goal is $y$ .

  $2x+3y=1037$   .... (1)

Total no of field goal $=517$ . Thus, $x+y=517$

Rewrite the equation in terms of $y$ .

  $y=517-x$   .... (2)

Now, substitute the value of $y$ in the equation (1) and solve for $x$ .

  $\begin{array}{c}2x+3\left(517-x\right)=1037\\ 2x+1551-3x=1037\\ -x=1037-1551\\ -x=-514\\ x=514\end{array}$

Substitute $x$ in the equation (2).

  $\begin{array}{c}y=517-514\\ =3\end{array}$

Hence, the required number of 2 point field goal is 514 and 3 point field is 3.