Respuesta :
Answer:
The number of free throws, two-point throw, and three-point throw are 135, 173, and 111 respectively.
Step-by-step explanation:
Let x,y, and z are the numbers of two-point field goals, numbers of three-point field goals, and the number of free-throws (one-point goal) respectively.
The total points= 814
[tex]\Rightarrow 2x+3y+z=814\;\cdots(i)[/tex]
As the number of two-point  goals was 49 less than double the number of three-point field goals she made.
[tex]\Rightarrow x=2y-49 \;\cdots(ii)[/tex]
Again, the number of free goals was 38 less than the number of two-point field goals she made.
[tex]\Rightarrow z=x-38\;\cdots(iii)[/tex]
From equations (i) and (iii)
2x+3y+x-38=814
[tex]\Rightarrow 3x+3y=852[/tex]
[tex]\Rightarrow x+y=284[/tex]
[tex]\Rightarrow 2y-49+y=284[/tex] [using equation (ii)]
[tex]\Rightarrow 3y=333[/tex]
[tex]\Rightarrow y=111[/tex]
From equation (ii),
[tex]x= 2\times111-38=173[/tex]
From equation (iii),
[tex]z=173-38=135[/tex].
Hence,
The number of free throws, z= 135
The number of two-point throw, x=173
The number of three-point throw, y=111.
