SOLUTION: An ice cream vendor sells an average of 100 cones per day when the price of each cone is $10.00. The vendor believes that for each 50 – cents drop in the price, she will sell 20 mo

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: An ice cream vendor sells an average of 100 cones per day when the price of each cone is $10.00. The vendor believes that for each 50 – cents drop in the price, she will sell 20 mo      Log On


   

Question 883703: An ice cream vendor sells an average of 100 cones per day when the price of each cone is $10.00. The vendor believes that for each 50 – cents drop in the price, she will sell 20 more cones. What should the price of the cones be if she wants a revenue of $1440?
Pls. Show me the solutions. May thanks
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
____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%2F0.5=-40.
A point known, as well as others, is (10,100).
y = How many cones sold.
y-100=-40%28x-10%29 in point-slope form.
y-100=-40x%2B400
highlight_green%28y=-40x%2B500%29.

REVENUE: This is QuantitySold%2APrice.
Quantity Sold = y
Price = x
Revenue is y%2Ax=%28-40x%2B500%29%2Ax, but we are then really focusing on the function %28-40x%2B500%29%2Ax and want to equate this revenue expression (function) to $1440.

highlight_green%28-40x%5E2%2B500x=1440%29.
Simplify.
-4x%5E2%2B50x=144
-2x%5E2%2B25x-72=0
highlight_green%282x%5E2-25x%2B72=0%29

Quadratic Formula Solution:
D=25%5E2-4%2A2%2A72=625-8%2A72=49, the discriminant
x=%2825%2B-+7%29%2F4
x=18%2F4=9%2F2=highlight%284.5%29
OR
x=32%2F4=highlight%288.0%29
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Either of the two prices, $4.50 or $8.00 per cone would be expected to give the revenue 1440 dollars.