# Problem of the Day

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

A.

B. or

C. or

D.

E. Â

Reveal Answer

### Solution

[latexpage]

If David is selling $65-5x$ baskets at $x$ dollars per basket, then his total revenue is $x(65-5x)$. We want to know the values of $x$ for which this revenue will exceed $150$. Thus,

$x(65-5x)>150$

$-5x^2+65x>150$

$-5x^2+65x-150>0$

$-5(x^2-13x+30)>0$

$x^2-13x+30<0$

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

By testing values, we can see that this final expression will be true for all values of $x$ such that $3<x<10$

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