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
![\Rightarrow 2x+3y+z=814\;\cdots(i)](https://tex.z-dn.net/?f=%5CRightarrow%202x%2B3y%2Bz%3D814%5C%3B%5Ccdots%28i%29)
As the number of two-point goals was 49 less than double the number of three-point field goals she made.
![\Rightarrow x=2y-49 \;\cdots(ii)](https://tex.z-dn.net/?f=%5CRightarrow%20x%3D2y-49%20%5C%3B%5Ccdots%28ii%29)
Again, the number of free goals was 38 less than the number of two-point field goals she made.
![\Rightarrow z=x-38\;\cdots(iii)](https://tex.z-dn.net/?f=%5CRightarrow%20z%3Dx-38%5C%3B%5Ccdots%28iii%29)
From equations (i) and (iii)
2x+3y+x-38=814
![\Rightarrow 3x+3y=852](https://tex.z-dn.net/?f=%5CRightarrow%203x%2B3y%3D852)
![\Rightarrow x+y=284](https://tex.z-dn.net/?f=%5CRightarrow%20x%2By%3D284)
[using equation (ii)]
![\Rightarrow 3y=333](https://tex.z-dn.net/?f=%5CRightarrow%203y%3D333)
![\Rightarrow y=111](https://tex.z-dn.net/?f=%5CRightarrow%20y%3D111)
From equation (ii),
![x= 2\times111-38=173](https://tex.z-dn.net/?f=x%3D%202%5Ctimes111-38%3D173)
From equation (iii),
.
Hence,
The number of free throws, z= 135
The number of two-point throw, x=173
The number of three-point throw, y=111.