SOLUTION: Please help me solve this problem. A land investment company purchase a parcel of land for $7200. After having sold all but 20 acres at a profit of $30 per acre over original cost

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Question 459572: Please help me solve this problem. A land investment company purchase a parcel of land for $7200. After having sold all but 20 acres at a profit of $30 per acre over original cost per acre, the company regained the entire cost of the parcel. How many acres were sold?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A land investment company purchase a parcel of land for $7200.
After having sold all but 20 acres at a profit of $30 per acre over original
cost per acre, the company regained the entire cost of the parcel.
How many acres were sold?
:
Let x = no. of acres sold
then
(x+20) = total no. of acres in the parcel
:
Selling price - cost price = $30
7200%2Fx - 7200%2F%28%28x%2B20%29%29 = 30
:
multiply by x(x+20), results:
7200(x+20) - 7200x = 30x(x+20)
7200x + 144000 - 7200x = 30x^2 + 600x
A quadratic equation
30x^2 + 600x - 144000 = 0
Simplify, divide by 30
x^2 + 20x - 4800 = 0
Factor this to
(x+80)(x-60) = 0
positive solution
x = 60 acres sold
:
:
Check this (total acres 20 more, 80)
7200%2F60 - 7200%2F80 =
$120 - $90 = $30; confirms our solution of x=60