Free-Throw Problem by the MC2 Mathematicians
Gina, who likes math and who can do mental math pretty well, plays for the 8th grade basketball team at her school. During one of the basketball games Gina was fouled while taking a shot. Even though she missed the shot she got to shoot two free throws. Going to the line to shoot the free throws Gina knew that so far this season she has made 78% of her free throws shots (using the usual rules for rounding). Gina missed the first free throw, but made the second one. Running back to play defense, Gina quickly calculated in her head that her free-throw shooting percentage had changed to 76% (after rounding).
From the information in this problem, can the number of free-throw shots made and the number of freethrow shots attempted this season by Gina be determined? If so, how, and what are they? If not, why not? Give a convincing argument to someone who is skeptical of your answer.
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