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The net profit that Ann makes from selling x pillows is give [#permalink]
06 Apr 2018, 15:34

Expert's post

00:00

Question Stats:

55% (00:25) correct
44% (01:06) wrong based on 9 sessions

The net profit that Ann makes from selling x pillows is given by the expression \(x^2 - 2x - 288\).

Quantity A

Quantity B

The number of pillows that Ann must sell for her net profit to be zero

20

A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.

Re: The net profit that Ann makes from selling x pillows is give [#permalink]
17 Apr 2018, 02:08

1

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All that is asked here is solve the given equation \(x^2 - 2x - 288 = 0\) By simplification, \(X^2 -18x + 16x -288 = 0\) Hence, \(x(x-18) +16(x - 18) = 0\) Therefore, \(x = -16,18\) However the value of x cannot be \(-\)ve since the number of pillows sold cannot be negative Hence, \(x =18\) < Qty B
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Re: The net profit that Ann makes from selling x pillows is give [#permalink]
18 Apr 2018, 15:36

Expert's post

Explanation

Set the expression equal to zero and then factor it.

You are looking for factors of 288 that have a difference of 2.

So find the integer factor pairs, starting with 1: 1 and 288; 2 and 144; 3 and 96; 4 and 72; 6 and 48; 8 and 36; 9 and 32; 12 and 24; 16 and 18.

The last pair you found works, so the factored form of your equation is: (x – 18)(x + 16) = 0. The solutions are 18 and –16, but obviously Ann cannot sell a negative number of pillows. The answer is choice (B).
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