Answer
No. of Free Throws : $594$
No. of two point field goals : $566$
No. of three point field goals :$145$
Work Step by Step
Let No. of free (one point) throws be $x$
No. of two point field goals be $y$
No. of three point field goals be $z$
Given,
Total points $=2161$
$x+2(y)+3(z)= 2161$
$x+2y+3z=2161$ Equation $(1)$
No. of free throws $=$ 14 more than four times the No. of three point field goals.
$x=4z+14$ Equation $(2)$
No. of two point field goals $=28$ less than the No. of free throws.
$y=x-28$ Equation $(3)$
From Equation $(2)$ and Equation $(3)$
$y=x-28$
$y=4z+14-28$
$y=4z-14$
$x+2y+3z=2161$
$4z+14+2(4z-14)+3z=2161$
$4z+14+8z-28+3z=2161$
$15z-14=2161$
$15z=2175$
$z=145$
Substituting $z$ value in Equation $(2)$
$x=4z+14$
$x=4(145)+14$
$x=580+14$
$x= 594$
Substituting $x$ value in Equation $(3)$
$y=x-28$
$y=594-28$
$y=566$
No. of Free Throws : $594$
No. of two point field goals : $566$
No. of three point field goals :$145$
