Problem of the Day

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. $5<x<6$

Reveal Answer

Answer

[latexpage]

D. $3<x<10$

See the Solution

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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