Solve the problem
-A basketball player scored 22 points in a game. The number of three-point field goals the player made was 12 less than three times the number of free throws (each worth 1 point). Twice the number of two-point field goals The player made was 5 more than the number of three-point field goals made. Find the number of free-throws, Two-point field goals, and three-point field goals that the player made in the game.
A)5 free throws; 3 two-point field goals; 4 three-point field goals
B)6 free throws; 4 two-point field goals; 6 three-point field goals
C)5 free throws; 5 two-point field goals; 5 three-point field goals
D)5 free throws; 4 two-point field goals; 3 three-point field goals

Question

Quizplus · Accepted Answer

The player scored a total of 22 points. Let the number of free throws be $f$, two-point field goals be $t$, and three-point field goals be $th$. The equations based on the given information are:1. $f + 2t + 3th = 22$ (Total points scored)2. $th = 3f - 12$ (Three-point field goals are 12 less than three times the number of free throws)3. $2t = th + 5$ (Twice the number of two-point field goals is 5 more than the number of three-point field goals)Substituting the second equation into the first gives a system of equations in terms of $f$ and $t$. Solving these equations yields $f = 5$, $t = 4$, and $th = 3$, which matches option D.

Solve the Problem -A Basketball Player Scored 22 Points in a Game. the a Game