Question

Samuel would like to rent a booth at his local farmer's market to sell his merchandise. It costs $300 to rent a booth at the farmer's market, and for each item that Samuel sells, x, he profits $25. This can be modeled by the function S(x) = 25x − 300. Based on the graph of the linear function that represents the amount of money Samuel profits, S(x), what is the coordinate of the x-intercept and its interpretation?

A. (12, 0); After selling 12 items, Samuel will have a positive profit.
B. (25, 0); After selling 25 items, Samuel will have a positive profit.
C. (300, 0); After selling 300 items, Samuel will have a positive profit.
D. (−300, 0); Samuel will begin with a positive profit

Answer 1

The x-intercept of S(x), along with it's correct interpretation, is given by the following option:

A. (12, 0); After selling 12 items, Samuel will have a positive profit.

What is the x-intercept of a function S(x)?

The x-intercept of a function S(x) is the value, or the values, of x, for which S(x) = 0. The point is given by (x,0).

In this problem, the function is given by:

S(x) = 25x - 300.

Hence the x-intercept is found as follows:

25x - 300 = 0.

25x = 300

x = 300/25

x = 12.

Hence the correct option is given by:

A. (12, 0); After selling 12 items, Samuel will have a positive profit.

More can be learned about x-intercepts at https://brainly.com/question/24388356

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