Real Estate: all but 20 ac sold at $30/ac profit, regaining

[zoya5972]

Hey! Havin a bit of trouble here... Help please!!!

A land investment company purchased a parcel of land for $7200. After having sold all but 20 acres ata profit of $30 per acre over the original cost per acre the company regained the entire cost of the parcel. How many acres were sold.

This is how i started breaking down the problem: If the total acres bought is say A and the total acres sold is X, then A=X+20, X=A-20, which should be the total acres sold.

I thought the formula for this problem could be, (Total acres sold) (Price per acre+ profit)= Cost of the parcel, (A-20) (x+30) = 7200

This where i get confused as to what i should be doing now. If i want to find the total acres sold, then i need to know the price per acre. How do i find them? HELP!!!!!

 

[Deleted member 4993]

Re: Real Estate

Hey! Havin a bit of trouble here... Help please!!!
A land investment company purchased a parcel of land for $7200. After having sold all but 20 acres ata profit of $30 per acre over the original cost per acre the company regained the entire cost of the parcel. How many acres were sold.

This is how i started breaking down the problem:
If the total acres bought is say A and the total acres sold is X, then
A=X+20
X=A-20, which should be the total acres sold.

I thought the formula for this problem could be,
(Total acres sold) (Price per acre+ profit)= Cost of the parcel
(A-20) (x+30) = 7200

This where i get confused as to what i should be doing now. If i want to find the total acres sold, then i need to know the price per acre. How do i find them? HELP!!!!!

Purchasing price /Acre = 7200/A

Selling price/acre = purchasing price + 30 = 7200/A + 30

Total money received = X * (7200/A + 30)= X * [7200/(X-20) + 30]

company regained the entire cost of the parcel

7200 = X * [7200/(X-20) + 30]

Solve for X

 

[Denis]

Re: Real Estate

Zoya, when you're confused by a problem, good idea is make one up, similar but SIMPLE; example:

|50|50|50|50|50|50| : bought 6 acres @ $50 each, total $300
|75|75|75|75| : sold 4 acres @ $75 each, total $300

Company bought A acres for total of $300.
Company sold (A-2) acres at $25 profit per acre, for total of $300.

Solve that, then solve the "biggy" the same way...kapish?

 

[zoya5972]

Re: Real Estate

thank you guys,

I used a bit of both suggestions and came out with Sold acres x (selling price + 30) should be equal to original cost price of the land $7200.

After several attempts found out that if X number of acres was purchased at $90 per acre for a total of $7200. Then,

Sold acres (selling price + profit)=7200

60(90+30)=7200

7200=7200

therefore the total number of acres bought was 80 for a price of $90 per acre. Of this 60 acres was sold for $120 per acre.

Question: Is there an easier formula for finding the total sold acres and the selling price.

 

[Denis]

Re: Real Estate

A land investment company purchased a parcel of land for $7200. After having sold all but 20 acres ata profit of $30 per acre over the original cost per acre the company regained the entire cost of the parcel. How many acres were sold.

a = acres purchased (?)
t = total purchase price ($7200)
n = acres not sold (20)
p = profit per acre (30)

purchase price per acre = t/a

(a - n)(t/a + p) = t : there is NO easier way!

You're given t,n,p : solve for a.

 

[mmm4444bot]

Re: Real Estate

Question: Is there an easier formula ... [?]

Answer: No.

Reason: That method is already easy.

... After several attempts found out that if X number of acres was purchased at $90 per acre for a total of $7200.

Comment: Your initial reasoning is sound; you just got confused with multiple symbols. If you had written an equation in one variable in your first step, then you would have solved that variable for the total number of acres in the parcel. Everything else would have followed from that. You only need one approach, and you were on it.

... This is how i started breaking down the problem:
If the total acres bought is say A and the total acres sold is X, then
A=X+20
X=A-20, which should be the total acres sold.

I thought the formula for this problem could be,
(Total acres sold) (Price per acre+ profit)= Cost of the parcel
(A-20) (x+30) = 7200 ...

You wrote x + 3, which means the total number of acres sold by the investors plus $30. (Ooops. You added the acres count to an amount of money.)

Here's a thought. Try to make things easier by concentrating on how different things can be written in terms of a single symbol. Use your same strategy, but instead of using two different symbols (eg: X and A) use A to represent the total number of acres in the parcel.

Then, A - 20 equals the number sold, and 7200/A equals the price paid by the investor for each acre.

Now there is no clumsy X, and you go straight to an equation that contains only one variable.

(A - 20) * (7200/A + 30) = 7200

See? It looks exactly like your original attempt, with the corrected expression for money (7200/A). Silly algebra and arithmetic mistakes excepted, there is only one attempt required to find A from this point forward.

Cleary, once you know that the parcel contains A = 80 acres, everything else follows from there.

Cheers,

~ Mark

 

[zoya5972]

Re: Real Estate

Thank you... it makes a lot more sense now...

(A-20) (7200/A+30)=7200
(A-20)((7200+30A)/A)= 7200
(A-20)(7200+30A)=7200A

7200A+30A^2-14400-600A=7200A

30A^2-14400-600A=0

A^2-20A-480=0 (this is where i get stuck.. where to now?) :wink:

 

[Denis]

Re: Real Estate

(A-20) (7200/A+30)=7200
(A-20)((7200+30A)/A)= 7200
(A-20)(7200+30A)=7200A
7200A+30A^2-14400-600A=7200A
30A^2-14400-600A=0
A^2-20A-480=0

14400 should be 144000, so: A^2 - 20A - 4800 = 0
Factor: (A - ?)(A + ?) = 0

 

[zoya5972]

Re: Real Estate

Oopsy!Thanks Denis!

Now it makes sense : A^2-20A-4800=0

(A+60) (A-80) = 0

Thus the answer: sold acres=60 X120= $7200 YAYYY!!!

Thank you all!

 

[Denis]

Re: Real Estate

Oopsy!Thanks Denis!
Now it makes sense : A^2-20A-4800=0
(A+60) (A-80) = 0
Thus the answer: sold acres=60 X120= $7200 YAYYY!!!
Thank you all!

Ya, but it's (A-60)(A-80) = 0 ; A = 60 or -80 ; A = 60 (-80 impossible) ; be careful, young one :wink:

 

[mmm4444bot]

Re: Real Estate

No, the answer is not $7200.

Please use complete sentences when reporting any answer to an applied math exercise (i.e., "word problem").

... Thus the answer: sold acres=60 X120= $7200

Answer: "The investors sold 60 acres."