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David decides to start a business making gift baskets. He estimates th

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New post 03 Dec 2019, 01:18
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David decides to start a business making gift baskets. He estimates that if he charges x dollars per gift basket, he will sell \(65-5x\) baskets per day. If his estimate is accurate, which of the following sets describes all values of x for which will he collect revenue in excess of $150 per day?

A. \(2<x<15\)

B. \(x<3\) or \(x>10\)

C. \(x<2\) or \(x>15\)

D. \(3<x<10\)

E. \(5<x<6\)


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Re: David decides to start a business making gift baskets. He estimates th  [#permalink]

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New post 03 Dec 2019, 02:28
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Bunuel wrote:
David decides to start a business making gift baskets. He estimates that if he charges x dollars per gift basket, he will sell \(65-5x\) baskets per day. If his estimate is accurate, which of the following sets describes all values of x for which will he collect revenue in excess of $150 per day?

A. \(2<x<15\)

B. \(x<3\) or \(x>10\)

C. \(x<2\) or \(x>15\)

D. \(3<x<10\)

E. \(5<x<6\)


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\(X*(65-5X)>150\)
\(65X-5X^2>150\)
\(5X^2-65X+150<0\)
\(X^2-13X+30<0\)
\((X-3)(X-10)<0\)
3<X<10
D:)
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Re: David decides to start a business making gift baskets. He estimates th  [#permalink]

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New post 03 Dec 2019, 03:12
we can solve linearly or plugin values of x= 4,5,6..9 we get revenue sales>180
IMO D


Bunuel wrote:
David decides to start a business making gift baskets. He estimates that if he charges x dollars per gift basket, he will sell \(65-5x\) baskets per day. If his estimate is accurate, which of the following sets describes all values of x for which will he collect revenue in excess of $150 per day?

A. \(2<x<15\)

B. \(x<3\) or \(x>10\)

C. \(x<2\) or \(x>15\)

D. \(3<x<10\)

E. \(5<x<6\)


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Re: David decides to start a business making gift baskets. He estimates th  [#permalink]

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New post 04 Dec 2019, 08:02
Bunuel wrote:
David decides to start a business making gift baskets. He estimates that if he charges x dollars per gift basket, he will sell \(65-5x\) baskets per day. If his estimate is accurate, which of the following sets describes all values of x for which will he collect revenue in excess of $150 per day?

A. \(2<x<15\)

B. \(x<3\) or \(x>10\)

C. \(x<2\) or \(x>15\)

D. \(3<x<10\)

E. \(5<x<6\)


\(PQ=R:x(65-5x)>150\)
\(5x^2-65x+150<0…x^2-13x+30<0\)
\((x-10)(x-3)<0…(less.than=inside.rng)…3<x<10\)

Ans (D)
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Re: David decides to start a business making gift baskets. He estimates th  [#permalink]

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New post 05 Dec 2019, 20:28
Bunuel wrote:
David decides to start a business making gift baskets. He estimates that if he charges x dollars per gift basket, he will sell \(65-5x\) baskets per day. If his estimate is accurate, which of the following sets describes all values of x for which will he collect revenue in excess of $150 per day?

A. \(2<x<15\)

B. \(x<3\) or \(x>10\)

C. \(x<2\) or \(x>15\)

D. \(3<x<10\)

E. \(5<x<6\)


Are You Up For the Challenge: 700 Level Questions


Using the formula revenue = price x number sold, we see that the revenue is x(65 - 5x), and we create the inequality:

x(65 - 5x) > 150

65x - 5x^2 - 150 > 0

Multiplying the inequality by -1, we have:

5x^2 - 65x + 150 < 0

x^2 - 13x + 30 < 0

(x - 3)(x - 10) < 0

We see that if 3 < x < 10, then (x - 3)(x - 10) would be negative, i.e., less than 0.

Answer: D
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Re: David decides to start a business making gift baskets. He estimates th   [#permalink] 05 Dec 2019, 20:28
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