An owner lists his home and agrees to pay a 6% commission provided that he nets $10,000 after paying the commission and the balance of his mortgage, which is $75,000. To the nearest dollar, what should the selling price be to net the owner his $10,000?

To determine the correct selling price that allows the owner to net $10,000 after paying a 6% commission and covering a mortgage balance of $75,000, we need to outline the earnings formula.

The owner wants to net $10,000 after paying a 6% commission, which means the earnings must account for both the mortgage payoff and the desired net amount. Let's break this down step-by-step.

First, let’s introduce some variables:

• Let ( S ) represent the selling price of the home.

• The total commission can be calculated as ( 0.06 \times S ).

• After the commission is deducted, the owner should have his net amount of $10,000.

The owner has to pay off the mortgage balance of $75,000, so the equation we can set up is:

[

S - (0.06 \times S) - 75,000 = 10,000

]

This can be simplified to:

[

S(1 - 0.06) - 75,000 = 10,000

]

[

0.94S - 75,000 = 10,000

]

Adding $75,000 to both sides