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Algebra / Linear functions Difficulty: Hard

For groups of $25$ or more people, a museum charges $dollar sign 21$ per person for the first $25$ people and $dollar sign 14$ for each additional person. Which function $f$ gives the total charge, in dollars, for a tour group with $n$ people, where $n greater than or equals 25$ ?

$f (n) = 14 n + 175$

$f (n) = 14 n + 525$

$f (n) = 35 n - 350$

$f (n) = 14 n + 21$

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Explanation

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

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.