A seller wants to net $10,000 after the broker's commission of 6% and a loan balance of $250,000 are paid. For how much does the property need to sell?

To determine the amount for which the property needs to sell so that the seller nets $10,000 after paying a 6% broker's commission and a loan balance of $250,000, you start by defining the variables involved in the transaction.

Let ( P ) represent the selling price of the property. The broker's commission is calculated as 6% of the selling price, which can be represented as ( 0.06P ). After the commission is deducted from the selling price, the amount available to the seller before paying off the loan balance is ( P - 0.06P ) or ( 0.94P ).

Next, the seller has to pay off the loan balance of $250,000. Thus, the remaining amount after paying the loan will be expressed as ( 0.94P - 250,000 ). The seller wants to net $10,000, so you can set up the equation:

[

0.94P - 250,000 = 10,000

]

Solving this equation will lead to the required selling price:

1. First, add $250,000 to both sides to isolate the term involving ( P ):

[