Question 883703
____y_________________x
Cones Sell__________Price
100_________________10.00
100+20_______________9.50
100+2*20____________10.00-2*0.50
100+3*20____________10.00-3*0.50


The slope is {{{m=-20/0.5=-40}}}.
A point known, as well as others, is (10,100).
y = How many cones sold.
{{{y-100=-40(x-10)}}} in point-slope form.
{{{y-100=-40x+400}}}
{{{highlight_green(y=-40x+500)}}}.


REVENUE:  This is {{{QuantitySold*Price}}}.
Quantity Sold = y
Price = x
Revenue is {{{y*x=(-40x+500)*x}}}, but we are then really focusing on the function {{{(-40x+500)*x}}} and want to equate this revenue expression (function) to $1440.


{{{highlight_green(-40x^2+500x=1440)}}}.
Simplify.
{{{-4x^2+50x=144}}}
{{{-2x^2+25x-72=0}}}
{{{highlight_green(2x^2-25x+72=0)}}}


Quadratic Formula Solution:
{{{D=25^2-4*2*72=625-8*72=49}}}, the discriminant
{{{x=(25+- 7)/4}}}
{{{x=18/4=9/2=highlight(4.5)}}}
OR
{{{x=32/4=highlight(8.0)}}}
-
Either of the two prices, $4.50 or $8.00 per cone would be expected to give the revenue 1440 dollars.