In basketball, a free throw is 1 point and a field goal is either 2 points or 3 points... WHOLE PROBLEM IN DESCRIPTION WOULDN'T FIT HERE SORRY

Question

In basketball, a free throw is 1 point and a field goal is either 2 points or 3 points. Suppose a professional basketball player scored a total of 1938 points in one season. The total number of 2-point field goals and 3-point field goals was 701, and he made 475 of the 557 free throws that he attempted. Find the number of 2-point and 3-point field goals the player made that season.

 

The class is meant to solve using substitution or elimination methods.

Answer 1

Let x = the number of 2-point shots and y = the number of 3-point shots

 

2x + 3y + 475  = 1938

2x + 3y = 1508  (equation #1)

x + y = 701  (equation #2)

 

Multiply equation #2 by -2 and add it to equation #1.

 

 2x + 3y = 1508

 -2x -2y = -1402     

           y = 106       Substitute this answer into equation #2

 

x +106 = 701

          x = 595

 

So, he made 106 3-point field goals and 595 2-point field goals.