SOLUTION: Help...I am drowning in this pool question.... Tropical pools figures that its monthly revenue on the sale of �x� pools is given by R = 1500x � 3x2 where �x� is less than 25. Wh

Question 59885This question is from textbook Elementry and Intermediate algebra
: Help...I am drowning in this pool question....
Tropical pools figures that its monthly revenue on the sale of �x� pools is given by R = 1500x � 3x2 where �x� is less than 25. What number of pools sold will provide revenue of $17,568? This question is from textbook Elementry and Intermediate algebra

Answer by chitra(359) (Show Source): You can put this solution on YOUR website!
It is given that the monthly revenue on the sale of "x" pools is given by the

equation:

R = 1500x - 3x^2 -------------- (1) and also

x < 25 --------------- (2)

And the total revenue for the month is given by : R = $ 17,568

Substituting for the value of R in the Equation (1), we get:

17,568 = 1500x - 3x^2

Adding 3x^2 - 1500 x on both sides of the above equation, we get:

3x^2 - 1500x + 17568 = 0

We solve this by the method of Factorization.

We shall divide the entire equation by 3 inorder to make the factorization

simpler.

x^2 - 500x + 5876 = 0

On factorization, we get:

x^2 - 488x - 12x + 5856 = 0

x(x - 488) - 12(x - 488) = 0

(x - 12)(x - 488) = 0

This implies x = 12 and x = 488

But, the according to the data x < 25

Thus the value of x = 12.

Hence, in order to obtain the revenue of $17568, 12 pools are to be sold.

HAPPY CALCULATING!!!

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