Context: For groups of $25$ or more, a museum charges $28 per person for the first $25$ people and $17 for each additional person. We need the total-charge function $f$ for a group of $n$ people, where $n \ge 25$.

Answer: A) $f(n) = 17n+275$

Why: The first $25$ people cost $28 \times 25 = 700$ dollars. Beyond them there are $n - 25$ additional people at $17 each, so $f(n) = 700 + 17(n - 25) = 700 + 17n - 425 = 17n + 275$. Check: $f(25) = 425 + 275 = 700$, exactly the flat cost of the first $25$ people.

Traps:

• B) Adds a single $28 admission instead of the $700 charge for the whole first block: $f(25) = 453 \ne 700$.
• C) Charges $17 to all $n$ people on top of the $700, double-counting the first $25$: $f(25) = 1125 \ne 700$.
• D) Comes from charging $28 + 17 = 45$ dollars per additional person: $700 + 45(n - 25) = 45n - 425$; it happens to match at $n = 25$ but gives $f(26) = 745$ instead of $717$.