A basketball player scored 29 points in a game. The number of three-point field goals the player made was 29 less than three tim
es the number of free throws (each worth 1 point). Twice the number of two-point field goals the player made was 15 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-10 free throws; 1 two-point field goals; 8 three-point field goals
B-11 free throws; 8 two-point field goals; 4 three-point field goals
C-10 free throws; 9 two-point field goals; 3 three-point field goals
D-10 free throws; 8 two-point field goals; 1 three-point field goals
If you let x represent the number of free throws. let y represent the number of two-point field goal. let z represent the number of three-point shots made.
Then the correct system of linear equations is as follows:
x + 2y + 3z = 29 (The total number of points scored is 29.) z = 3x - 29 (The number of 3-pointers was 29 less than 3 times the number of free throws.) 2y = z + 15 (Twice the number of 2-point shots made was 15 more than the number of 3-pointers.)
Solution: This basketball player scored 10 points via free throws (10 at 1 point each), 16 points via 8 two-point shots made, and 3 points via 1 three-point shots made. So, in the choice its letter D.
