a basketball players free - throw percentage is the ratio of the number of successful shots made to the…
a basketball players free - throw percentage is the ratio of the number of successful shots made to the number of shots attempted. a basketball player has made 13 of the first 20 free throws she has attempted this season. which rational expression can be used to find the free throw percentage for the season if she successfully makes her next x free - throw attempts?\n\\(\\frac{13x}{20x}\\)\n\\(\\frac{13 + x}{20 + x}\\)\n\\(\\frac{13 + x}{20}\\)\n\\(\\frac{13}{20 + x}\\)
Answer
Explanation:
Step1: Recall free - throw percentage formula
Free - throw percentage = $\frac{\text{Number of successful shots}}{\text{Number of shots attempted}}$.
Step2: Calculate new number of successful shots
The player made 13 successful shots initially and makes $x$ more successful shots. So the new number of successful shots is $13 + x$.
Step3: Calculate new number of attempted shots
The player attempted 20 shots initially and attempts $x$ more shots. So the new number of attempted shots is $20 + x$.
Step4: Form the rational expression
The free - throw percentage is $\frac{13 + x}{20 + x}$.
Answer:
$\frac{13 + x}{20 + x}$ (corresponding to the second option in the multiple - choice question)