by the way I posted this in urgent help but I think it was moved...anyway this is sort of urgent, I need a fully worked out solution soon
so anyone who can help would be appreciated!!
i received this problem and worked through it, but my solution is flawed! it seems to be a pretty backwards solution.
The Problem
While watching a basketball game one day on television, I saw the following situation:
A player was fouled as he drove for the basket. At the bottom of the screen, it was stated that "Player X is making 78% of his free throws". The player missed the first free throw and made the second.
Later in the game, the player was again fouled. This time, at the bottom of the screen, it said "Player X is making 76% of his free throws". The statistic had been updated after his first two attempts.
Recognizing that the percentages presented on the screen were rouded to the nearest 1%, how many free throws had player X attempted and how many had he made? Be sure to find all possible solutions (if any).
My Bad Solution
First, I named things.
# Made at first statistic=f
% Made at first statistic=0.78f
# Attempted at 2nd stat=f+2
% Made at 2nd stat=0.76(f+2)
# Made at 2nd stat=0.78f+1
Then I made a plan.
# Made @ 1st stat + # made in game = 76% of attempts @ 2nd stat
0.78f+1=0.76(f+2)
SOLVE FOR F (# attempted @ 1st stat)
f=26
SO...
26 attempted at first stat
20 made
28 attempted at second stat
21 made
Right?? well...not really...
The Issue
78% of 26=20.28
20/26 rounds to 0.77 (wrong percentage)
76% of 28=21.28
21/28 rounds to 0.75 (wrong again)
the solution works when rounded from percentages to shots, but not from shots to percentages.
I need to find a solution in which the set considered for shots is whole numbers and I think I need a solution with graphs and zeros so I can be sure I can solve for all possible solutions (if there is more than one).
I'm stumped so any help is appreciated!!
-Mike
Let be the total number of shots he made out of shots before he made the two shots.
thus, ..................(1)
also, after he made the two shots, he made shots in total. since he missed one, the number of shots he made becomes . at the end, he made 76% of his shots, so that
...................(2)
thus you have two equations and two unknowns. you can solve for and
Yes but how is this rounding problem solved? the problem states that it will be rounded to the nearest 1%, which is a terrible coincidence for the numbers given (actually, I think the teacher did this on purpose to force us to use a different method to solve the problem)
oh yeah I thought that but I solved through anyway to see if it would be right, let me try this again
You have a pair of inequalities defined by this problem:
and:
Each of these defines a region between a pair of lines in the first quadrant, and all integer grid points in the region where these regions overlap are feasible solutions. This is a closed region in the form of a parallelogram.
RonL
I need a little help solving this however.
I put all the inequalities in terms of m (so 4 inequalities)
so this is what I had:
m<0.785a
m(>or=)0.775a
m<0.765a+0.53
m(>or=)0.755a+0.51
(i switched around the < and the (<or=) symbols because i thought you made a typo)
i used the inequality application on my TI-84 Plus and graphed where the shades intersect, but I'm not sure how to find integer points within the defined region
I would do it by search, the largest value that can take is less than , and the smallest more than (find the points of intersection of the lines defining the feasible region to show this).
So for each between and I would check which values of give points in the feasible region (they will all be close to ).
RonL