Final answer:
Kevin Durant made 703 free throws, 657 two-point field goals, and 192 three-point field goals during the 2013-2014 NBA season by setting up and solving an equation based on the given point values and relationships between his types of scores.
Step-by-step explanation:
We are given that Kevin Durant scored a total of 2593 points during the 2013-2014 regular NBA season. The number of his free throws was 127 more than three times the number of his three-point field goals, and his two-point field goals were 46 less than his free throws.
Let's denote the number of three-point field goals as x. Thus, the number of free throws is 3x + 127 and the number of two-point field goals is 3x + 127 - 46, which simplifies to 3x + 81.
Since each free throw is worth one point, three-point field goals are worth three points each, and two-point field goals are worth two points each, we can set up the following equation to represent the total points:
Total points = Free throws + 2*(Two-point field goals) + 3*(Three-point field goals)
Substituting the expressions we have for free throws, two-point field goals, and three-point field goals in terms of x gives us:
2593 = (3x + 127) + 2*(3x + 81) + 3*x
Now we can solve for x which represents the number of three-point field goals:
2593 = 3x + 127 + 6x + 162 + 3x
2593 = 12x + 289
2304 = 12x
x = 192
So, Kevin Durant made 192 three-point field goals.
Now, we can find the number of free throws and two-point field goals made:
Free throws = 3*192 + 127 = 576 + 127 = 703
Two-point field goals = 703 - 46 = 657
Therefore, Kevin Durant made 703 free throws, 657 two-point field goals, and 192 three-point field goals during the 2013-2014 NBA season.