SOLUTION: A sporting goods store sells 90 fishing rods in a season for $200 each. Each $10 decrease in price would result in five more rods being sold. Calculate the number of rods sold and

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Question 1151555: A sporting goods store sells 90 fishing rods in a season for $200 each. Each $10 decrease in price would result in five more rods being sold. Calculate the number of rods sold and the selling price to generate a revenue of $17 600 from sales of fishing rods.
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
.

According to the condition, the number of rods sold as a function of price "p" is


    n(p) = 90 + %285%2F10%29%2A%28200-p%29,   

or, equivalently,

    n(p) = 90 + 0.5*(200-p).


The revenue R(p)  as the function of price is then the product


    R(p) = p*n(p) = p*(90 + 0.5*(200-p) = p*(90 + 100 - 0.5*p) = -0.5p^2 + 190p.


To generate the revenue of 17600 dollars, the price should satisfy this equation


    R(p) = 17600 dollars,

or, equivalently

    -0.5p^2 + 190p = 17600.


Simplify and solve for p.


    p^2 - 380p + 35200 = 0

    p%5B1%2C2%5D = %28380+%2B-+sqrt%283800%5E2+-+4%2A35200%29%29%2F2 = %28380+%2B-+60%29%2F2.


ANSWER.  There are two solutions: p= 160  and  p= 220  dollars.

Solved.



Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

A sporting goods store sells 90 fishing rods in a season for $200 each. Each $10 decrease in price would result in five more rods being sold. Calculate the number of rods sold and the selling price to generate a revenue of $17 600 from sales of fishing rods.
Four (4) $10 price reductions or a $40 reduction, or a reduced price of $160 (200 - 40) will yield sales of 20 (4 * 5) more rods or a total of 110 (90 + 20) rods in order to generate $17,600 in revenue.