A Basketball Question

Macjack452

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Joined
Jan 8, 2022
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13
Background:
Possession = end result is a FG or a FTP
FG = field goal
FTP = possession that ends in Free Throws
FTA = Free Throw attempts (these are worth 0.475 FTP)

If I have 100 possessions and I know the FTA/FG ratio is 33.3% how do I solve for FG and FTP?
I want to know how many of those 100 possessions ended in FGs and how many ended in FTPs.

By hand I get something like 13.75 FTP and 86.25 FG but how do I figure this out mathematically?

thanks for any help!
 
Show us your work so we can help you. Read the posting guidelines.
 
FTA = Free Throw attempts (these are worth 0.475 FTP) [imath]\Rightarrow[/imath]FTA = .475 FTP[imath]\Rightarrow[/imath] FTP= FTA/.475---Equation(1)
FTA/FG ratio is 33.3% [imath]\Rightarrow[/imath] FTA/FG=1/3[imath]\Rightarrow[/imath] FG=3*FTA---Equation(2)
Possession = end result is a FG or a FTP [imath]\Rightarrow[/imath] Possession = 100 = FG +FTP---Equation(3)

It's a system of 3 equations and three unknowns (FTA, FG, FTP). Can you solve it?
 
FTA = Free Throw attempts (these are worth 0.475 FTP) [imath]\Rightarrow[/imath]FTA = .475 FTP[imath]\Rightarrow[/imath] FTP= FTA/.475---Equation(1)
FTA/FG ratio is 33.3% [imath]\Rightarrow[/imath] FTA/FG=1/3[imath]\Rightarrow[/imath] FG=3*FTA---Equation(2)
Possession = end result is a FG or a FTP [imath]\Rightarrow[/imath] Possession = 100 = FG +FTP---Equation(3)

It's a system of 3 equations and three unknowns (FTA, FG, FTP). Can you solve it?
I don’t know that’s why I’m asking! I do see now how it’s 3 equations.
 
I don’t know that’s why I’m asking!
And I've given you an answer on how to start.

I do see now how it’s 3 equations.
I think you meant to say "I do NOT see how it's 3 equations" I labelled them for you Equation(1), Equation(2), Equation(3).
Another hint: substitute equations 1 and 2 into equation 3 in terms of FTA

At least show some effort and try to solve it. In the end it's your problem, not ours :)
 
And I've given you an answer on how to start.


I think you meant to say "I do NOT see how it's 3 equations" I labelled them for you Equation(1), Equation(2), Equation(3).
Another hint: substitute equations 1 and 2 into equation 3 in terms of FTA

At least show some effort and try to solve it. In the end it's your problem, not ours :)
Ok so I think I misspoke. FTP actually = .475 FTA so that makes equation 1 -> FTP = FTA*.475

Now subbing equations 1 and 2 into equation 3 I get 100 = 3*FTA + .475*FTA or 100 = 3.475FTA.
Then solve for FTA = 100/3.475

So FTA = 28.77

Now plug into equation 2 to get FG -> FG =3*28.77

So FG = 86.31

Then I can either solve equation 1 using FTA or simply plug the FG value into equation three giving 100 = 86.31 + FTP so then FTP = 100 -86.31

FTP = 13.69

does this look correct? I think I got it now!
 
Ok so I think I misspoke. FTP actually = .475 FTA so that makes equation 1 -> FTP = FTA*.475

Now subbing equations 1 and 2 into equation 3 I get 100 = 3*FTA + .475*FTA or 100 = 3.475FTA.
Then solve for FTA = 100/3.475

So FTA = 28.77

Now plug into equation 2 to get FG -> FG =3*28.77

So FG = 86.31

Then I can either solve equation 1 using FTA or simply plug the FG value into equation three giving 100 = 86.31 + FTP so then FTP = 100 -86.31

FTP = 13.69

does this look correct? I think I got it now!
Correct. For practical reasons, you might want to round your answer to the closest integer, i.e. FTP=14 and FG=86.
 
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