The function P(n) = 14n - 210 gives a food truck's profit, in... | SAT Linear functions Question, Answer Explained

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The function $P(n) = 14n - 210$ gives a food truck's profit, in dollars, from selling $n$ sandwiches in one day. What is the best interpretation of $14$ in this context?

A

Each additional sandwich sold increases the truck's daily profit by $\$14$ .

B

The truck has $\$14$ in costs each day.

C

The truck must sell $14$ sandwiches to break even.

D

The truck's profit is $\$14$ if it sells $1$ sandwich.

Show answer and explanation

Answer: A

In $P(n) = 14n - 210$ , the coefficient $14$ is the slope, the change in profit for each increase of $1$ in $n$ . So each additional sandwich adds $\$14$ to the daily profit. The $-210$ shows that the truck loses $\$210$ on a day it sells no sandwiches.

Choice C confuses the slope with the break-even point. The truck breaks even when $14n = 210$ , at $n = 15$ sandwiches.

Why the other choices are wrong

B. The daily costs show up in the constant term. P(0) = -210, so the truck has $210 in costs.
C. Breaking even means P(n) = 0, which happens at n = 15, not 14.
D. P(1) = 14 - 210 = -196, so selling 1 sandwich gives a loss of $196, not a profit of $14.

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