Question

A property owner tells the listing agent that she would like to net $75,000 from the sale of her home. If the commission negotiated between the agent and seller is 7%, which of the following sales prices for the home would come closest to satisfying the owner's goal?

a) $1,200,000
b) $800,000
c) $1,000,000
d) $875,000

Answer 1

To determine the sales price that would come closest to satisfying the owner's goal of netting $75,000 from the sale of her home, we need to consider the commission negotiated between the agent and seller.

If the commission is 7% of the sales price, we can calculate the sales price that would result in a net amount of $75,000 after deducting the commission.

Let's calculate the sales prices for each option:

a) $1,200,000:

Commission = 7% of $1,200,000 = $84,000

Net amount = $1,200,000 - $84,000 = $1,116,000

b) $800,000:

Commission = 7% of $800,000 = $56,000

Net amount = $800,000 - $56,000 = $744,000

c) $1,000,000:

Commission = 7% of $1,000,000 = $70,000

Net amount = $1,000,000 - $70,000 = $930,000

d) $875,000:

Commission = 7% of $875,000 = $61,250

Net amount = $875,000 - $61,250 = $813,750

Among the given options, the sales price that comes closest to satisfying the owner's goal of netting $75,000 is:

d) $875,000

With a sales price of $875,000, the owner would have a net amount of $813,750 after deducting the 7% commission.

Answer 2

To determine the closest sales price that would allow the owner to net $75,000 after a 7% commission, we solved the equation 0.93x = $75,000, resulting in a sales price of approximately $80,645.16. The closest option available to this value is d. $875,000.

Step-by-step explanation:

To find the sales price that would allow the owner to net $75,000 after the agent takes a 7% commission, we can set up an equation. Let x represent the sales price. The net amount the owner wants to receive is the sales price minus the commission. The commission is 7% of the sales price, or 0.07x. Therefore, the equation we will solve for x is:

x - 0.07x = $75,000

Simplifying this, we get:

0.93x = $75,000

Now, dividing both sides by 0.93 gives us:

x = $75,000 / 0.93

x ≈ $80,645.16

Reviewing the options, the sales price closest to this calculated amount that would meet the owner's goal is $80,000, so the correct option is: d) $875,000