SOLUTION: I need help in trying to understand exactly what formula I need to find the answer to this problem. A real estate investor bought acreage for $7200. After reselling three-fourt

Algebra ->  Human-and-algebraic-language -> SOLUTION: I need help in trying to understand exactly what formula I need to find the answer to this problem. A real estate investor bought acreage for $7200. After reselling three-fourt      Log On


   

Question 398208: I need help in trying to understand exactly what formula I need to find the answer to this problem.
A real estate investor bought acreage for $7200. After reselling three-fourths of the acreage at a profit of $30 per acre, she recovered the $7200. How many acres did she sell?
Thank you for your help.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A real estate investor bought acreage for $7200. After reselling three-fourths of the acreage at a profit of $30 per acre, she recovered the $7200. How many acres did she sell?
------
Let original price per acre be "x"
Let the # of acres be "y"
---
unit price*# of acres = total price paid
-----------------------------
xy = 7200 dollars
--------------------------
When the price is x+30 and # of acres is (3/4)y you get:
(x+30)(3/4)y = 7200
=========================
Solve the system:
xy = 7200
(x+30)(3/4)y = 7200
----
y = 7200/x
Substitute for "y" and solve for "x":
(x+30)(3/4)(7200/x) = 7200
-----
(x+30)(1800/x) = 2400
---
(x+30)(3) = 4x
3x+90 = 4x
x = 90 acres (original number of acres)
(3/4)x = (3/4)90 = 67.5 (# of acres she sold)
==================================================
Cheers,
Stan H.