In basketball, there are 3-point shots, 2-point shots, and 1-point free throws. Josh scored 39 points in a game. He made the same number of 2-point shots as 3-point and free throws combined. He scored one more point on 3-pointers than he did on free throws. How many of each did he make?

Answer 1

Let
x1=number of 1-point shots
x2=number of 2-point shots
x3=number of 3point shots

"Josh scored 39 points in a game" =>
3x3+2x2+x1=39.........(1)

"the same number of 2-point shots as [3-point and free throws combined]"
x2=x3+x1 .............(2)

"scored one more point on 3-pointers than he did on free throws" =>
3x3-x1=1 .............(3)

Solve the system of equations:
Substitute (2) in (1)
3x3+2(x3+x1)+x1=39, simplify
5x3+3x1=39............(1a)
3 times (3):
9x3-3x1 =3 ............(3a)

(3a)+(1a)
14x3=42 => x3=3
Substitute x3 in (3)
3(3)-x1=1 => x1=8

substitute x3 and x1 in (1)
3(3)+2(x2)+8 = 39 =>
x2=(39-9-8)/2=11

So (x1,x2,x3)=(8,11,3)

Check answer by substituting values of x1,x2 and x3 into original equations.

Answer 2

2t + 3r + f = 39

t = r + f

3r - 1 = f

subs ... t = r + 3r - 1 = 4r - 1

subs ... 8r - 2 + 3r + 3r - 1 = 39

find r, then substitute back