SAT Question bbf9e5ce: Linear Functions answer and explanation with Desmos solution

Choice A is correct. A tour group with $n$ people, where $n\ge 25$, can be split into two subgroups: the first $25$ people and the additional $n-25$ people. Since the museum charges $$21$ per person for the first $25$ people and $$14$ for each additional person, the charge for the first $25$ people is $$21(25)$ and the charge for the additional $n-25$ people is $$14(n-25)$. Therefore, the total charge, in dollars, is given by the function $f(n)=21(25)+14(n-25)$, or $f(n)=14n+175$.