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