Answer:
Number of two point goals = 169
Number of three point goals = 123
Number of free throws = 139
Step-by-step explanation:
Let the number of two point goals = [tex]x[/tex]
Let the number of three point goals = [tex]y[/tex]
Let the number of free throws = [tex]z[/tex]
As per the given statements:
[tex]x = 2y-77 ...... (1)[/tex]
[tex]z = x-30 ...... (2)[/tex]
Using equation (1):
[tex]z = 2y-107[/tex] ...... (3)
Total number of points from two point goals = [tex]2x[/tex]
Total number of points from three point goals = [tex]3y[/tex]
Total number of points from free throws = [tex]z[/tex]
[tex]2x+3y+z=846[/tex]
using (1) and (3):
[tex]2(2y-77)+3y+2y-107=846\\\Rightarrow 4y-154+5y-107=846\\\Rightarrow 9y-261=846\\\Rightarrow 9y=846+261\\\Rightarrow 9y=1107\\\Rightarrow y =123[/tex]
By (1):
[tex]x = 2\times 123-77 =169[/tex]
By (3):
[tex]z =2\times 123-107 = 139[/tex]
So, answers are:
Number of two point goals = 169
Number of three point goals = 123
Number of free throws = 139
