MHB Real Estate math word problem help

[jmathdisinclined]

I am studying to take a real estate exam. I am having problems determining the correct formula on the percentage problems. I need help solving the answer and understanding the correct formula. Help is much appreciated. The math problem is:
The subject is a mixed use undeveloped property with 3 acres zoned commercial,
5 acres zoned multi-unit, and 2 acres zoned single-unit. A similar 10-acre property
recently sold for $1.80 per sf with 4 acres zoned commercial, 4 acres zoned multiunit,
and 2 acres zoned single-unit residential.

Based on this one sale property, what is the per square foot value of the subject
property if multi-unit land typically sells for 40% of commercial land prices, and
single-unit residential land sells for 20% of commercial land prices?

 

[HOI]

Let C be the cost of one acre of "commercial land". Since "multi-unit land typically sells for 40% of commercial land prices" one acre of "multi-unit land" cost .4C. Since "single-unit residential land sells for 20% of commercial land prices" one acre of single-unit residential land" cost .2C.

"A similar 10-acre property recently sold for 1.80 per sf with 4 acres zoned commercial, 4 acres zoned multi-unit, and 2 acres zoned single-unit residential."

There are 43560 square feet per acre so 1.80 per sf is (1.80)(43560)= 78408 per acre.

So 4C+ 4(.4C)+ 2(.2C)= 4C+ 1.6C+ .4C= 6C= 78408. C= 78408/6= 13068 . One acre zoned commercial costs 13068, one acre zoned multi-unit cost .4(13068)= 5227.20, and one acre zoned single unit residential costs .2(13068)= 2613.60.

The question asks for the cost of 3 acres zoned commercial, 5 acres zoned multi-unit, and 2 acres zoned single-unit.

That is 3(13068)+ 5(5227.20)+ 2(2613.60).

 

[jmathdisinclined]

Thank you Country Boy.

Great job, the answer of $1.62 per sf is correct. Now I will need to figure out how to memorize the way to solve this type of question. There are a few other practice questions I have. I will reverse engineer this equation, and hopefully after a few go through I will have it down. Your help is much appreciated.

Let C be the cost of one acre of "commercial land". Since "multi-unit land typically sells for 40% of commercial land prices" one acre of "multi-unit land" cost .4C. Since "single-unit residential land sells for 20% of commercial land prices" one acre of single-unit residential land" cost .2C.

"A similar 10-acre property recently sold for 1.80 per sf with 4 acres zoned commercial, 4 acres zoned multi-unit, and 2 acres zoned single-unit residential."

There are 43560 square feet per acre so 1.80 per sf is (1.80)(43560)= 78408 per acre.

So 4C+ 4(.4C)+ 2(.2C)= 4C+ 1.6C+ .4C= 6C= 78408. C= 78408/6= 13068 . One acre zoned commercial costs 13068, one acre zoned multi-unit cost .4(13068)= 5227.20, and one acre zoned single unit residential costs .2(13068)= 2613.60.

The question asks for the cost of 3 acres zoned commercial, 5 acres zoned multi-unit, and 2 acres zoned single-unit.

That is 3(13068)+ 5(5227.20)+ 2(2613.60).

 

[HOI]

Is "memorizing" all you can do? I recommend learning the basic definitions, tthen thinking!