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A pottery store owner determines that the revenue for sales

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A pottery store owner determines that the revenue for sales [#permalink] New post 14 May 2019, 08:40
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A pottery store owner determines that the revenue for sales of a particular item can be modeled by the function \(r(x)= 50 \sqrt{x} −40\), where x is the number of the items sold. How many of the items must be sold to generate $110 in revenue?

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9
[Reveal] Spoiler: OA

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Re: The graph above shows a parabola that is symmetric about the [#permalink] New post 14 May 2019, 08:53
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With all word problems start by skipping to the end to determine the sought value, in this case the number of items sold to generate $110 in revenue. Also, note that the choices are numeric values in numeric order, which indicates that both plugging in the choices and logical estimation are potential tactics. Now, we see the equation that revenue =50√x − 40.

First, recognize that in order to generate the integer value $110, then formula must result in an integer. Therefore, √x must be an integer, so logically eliminate choices A through D. Were you short on time on the exam, select choice E and move on.

However, you can also plug in choice E 9 to prove that it is correct. 50 x √9 = 150 and 150 - 40 = 110, which matches the conditions of the problem, so of course E is indeed correct.
Re: The graph above shows a parabola that is symmetric about the   [#permalink] 14 May 2019, 08:53
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A pottery store owner determines that the revenue for sales

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