In basketball, a free throw is 1 point and a field goal is either 2 or 3 points. In a recent season, Tim Duncan of the San Antonio Spurs scored a total of 1342 points. The total number of 2-point field goals and 3-point field goals was 517, and he made 305 of the 455 free throws that he attempted. Find the nu,ber of 2-point field goals and 3-point field goals Duncan made that season.
I just need to know the two equations and then I can solve it.
let the number of 2-pointers be x
let the number of 3-pointers be y
x+y = 517
2x + 3y + 305 = 1342
I got 514 2-pointers, only 3 3-pointers, and 305 free throws.
These answers check out, but must be false data, only 3 threepointers per season would be pretty poor shooting.
The data for Tim Duncan are probably correct. He plays center most of the time, and occasionally plays power forward. In these positions, he very seldom gets a chance to shoot from beyond the three point line, and probably would not want to if he did. So far in the 2007-2008 season, he has taken only one three-point shot, and missed it.
5x=3y+567
To solve for the number of 2-point and 3-point field goals made by Tim Duncan, we can set up two equations.
Let's say the number of 2-point field goals made by Duncan is 'x', and the number of 3-point field goals made by Duncan is 'y'.
1. The first equation represents the total points scored by Tim Duncan:
2x + 3y (points from field goals) + 305 (points from free throws) = 1342
This equation accounts for the total points scored by Duncan in a season, including both field goals and free throws.
2. The second equation represents the total number of field goals made by Duncan:
x (2-point field goals) + y (3-point field goals) = 517
This equation accounts for the total number of field goals made by Duncan, including both 2-point and 3-point shots.
Now you can solve this system of equations to find the values of 'x' and 'y'.