Chapter 12, Problem 16STP

To determine

To find: the $2$ -points and $3$ -points field goals did Casey make during the season.

Answer to Problem 16STP

Casey make $69$ , $2$ -points and $15$ , $3$ -points field goals.

Explanation of Solution

Given information:

Total fields goals $=84$ and total points $=183$

Calculation: To find the field goals,

Let $x$ represents the $2$ -points field goals and $y$ represents the $3$ -points field goals,

Since the total files goals $=84$ ,

  $x+y=84$

Total points $=183$ ,

  $2x+3y=183$

Now solve both equations,

  $\begin{array}{l}2x+3y=183\\ 2x+2y=168\text{ [multiply the eq 1 by 2]}\\ y=15\text{ [subtract both equations]}\\ 2x+2\left(15\right)=168\text{ [substitute]}\\ 2x+30=168\text{ [multiply]}\\ 2x=138\text{ [subtract]}\\ x=69\text{ [divide]}\end{array}$

Thus, Casey make $69$

  $2$ -points and $15$

  $3$ -points field goals.