Question

A real estate investor bought two parcels of land for $1,000,000. several years later, he sold these parcels for a $10,000 profit. one of these parcels was sold for a 1% loss the other was sold for a 4% profit. what was the purchase price of the land?

Answer 1

The purchase price of the land was $990,000.

Step-by-step explanation:

Total Profit = $10,000

Determine the individual profit or loss percentages for the two parcels.

Let the purchase price of one parcel be x.

One parcel was sold for a 1% loss:

Selling Price of this parcel = Purchase Price - 1% of Purchase Price

Selling Price = x - 0.01 * x = x * (1 - 0.01) = x * 0.99

The other parcel was sold for a 4% profit:

Selling Price of this parcel = Purchase Price + 4% of Purchase Price

Selling Price = x + 0.04 * x = x * (1 + 0.04) = x * 1.04

Calculate the total selling price from both parcels.

Total Selling Price = Selling Price of Parcel 1 + Selling Price of Parcel 2

Total Selling Price = x * 0.99 + x * 1.04

Total Selling Price = x * (0.99 + 1.04)

Total Selling Price = x * 2.03

Determine the total purchase price.

Total Selling Price = Total Purchase Price + Total Profit

x * 2.03 = Total Purchase Price + $10,000

We know Total Profit = $10,000, so rearrange the equation to find the Total Purchase Price:

Total Purchase Price = x * 2.03 - $10,000

Calculate the original purchase price of the land.

Total Purchase Price = $1,000,000 (as given) - Total Profit

Total Purchase Price = $1,000,000 - $10,000

Total Purchase Price = $990,000

Therefore, the original purchase price of the land was $990,000.

Answer 2

To find the purchase price of the land, you can set up a system of equations based on the given information. Once you solve the equations, you can find that the purchase price of the land is approximately $497,538.04.

Step-by-step explanation:

To find the purchase price of the land, we need to set up a system of equations based on the given information.

Let's say the purchase price of one parcel of land is x dollars. Since the other parcel was sold for a 1% loss, its selling price would be 0.99x dollars. On the other hand, the second parcel was sold for a 4% profit, so its selling price would be 1.04x dollars.

According to the given information, the investor sold both parcels for a $10,000 profit. Therefore, the equation can be set up as follows:

0.99x + 1.04x = $1,010,000

Combining like terms, we get:

2.03x = $1,010,000

Dividing both sides of the equation by 2.03, we find that the purchase price of the land is approximately $497,538.04.