Final answer:
By setting up a system of equations for the given ticket price totals and solving for the individual ticket prices, we determine the price per football ticket to be $115.718 and the price per basketball ticket to be $53.098. However, these results do not match any of the answer choices provided, suggesting there might be a mistake in the question or the calculation.
Step-by-step explanation:
To solve the problem of determining the individual ticket prices for football and basketball for the 2016-2017 NFL and NBA seasons, we need to set up a system of equations. Let's designate F as the price of a football ticket and B as the price of a basketball ticket.
According to the information provided:
- 3F + 2B = $425.35
- 4F + B = $501.97
To find the values of F and B, we can solve this system of equations using substitution or elimination. If we solve for B in the second equation (B = $501.97 - 4F), and substitute that into the first equation, we get 3F + 2($501.97 - 4F) = $425.35, which simplifies to 3F + $1003.94 - 8F = $425.35. This further simplifies to -5F = $425.35 - $1003.94, which yields F = $115.718 per football ticket.
Now we substitute F back into B = $501.97 - 4F to find B = $501.97 - 4($115.718) = $53.098 per basketball ticket.
However, when comparing these calculated prices to the options given, we can see that none of them exactly match our calculations. This indicates that there might have been an error in the provided question or in the calculation. As such, we do not have enough confidence in the correctness of any answer to the student's question.