An owner list his home and agrees to pay a 6% commission provided 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?
selling price = p
costs:
commission = .06 p
mortgage = 75,000
so
10,000 = p - .06 p -75,000
.94 p = 85000
p = 85,000/.94 = 90,425.53
To find the selling price that will enable the owner to net $10,000 after paying the commission and the balance of his mortgage, we need to work backwards. Let's break it down into steps:
Step 1: Calculate the commission amount.
Since the commission is 6% of the selling price, we can find it by multiplying the selling price by 6% (or 0.06).
Commission = Selling price * 0.06
Step 2: Calculate the remaining balance (after the mortgage is paid).
The remaining balance is the mortgage balance of $75,000 minus the commission amount.
Remaining balance = $75,000 - Commission
Step 3: Calculate the selling price that will leave the owner with $10,000.
To calculate the selling price, we need to find the sum of the remaining balance and the desired net amount ($10,000).
Selling price = Remaining balance + $10,000
Let's put it all together and calculate the selling price:
Commission = Selling price * 0.06
Remaining balance = $75,000 - Commission
Selling price = Remaining balance + $10,000
Now, we'll substitute the equations to find the selling price:
Commission = Selling price * 0.06
Remaining balance = $75,000 - Selling price * 0.06
Selling price = Remaining balance + $10,000
Let's solve these equations:
1. Commission = Selling price * 0.06
Commission / 0.06 = Selling price
2. Remaining balance = $75,000 - Selling price * 0.06
3. Selling price = Remaining balance + $10,000
We can substitute equation 2 into equation 3:
$75,000 - Selling price * 0.06 = Remaining balance + $10,000
Now, we can simplify the equation:
$75,000 - Selling price * 0.06 - Remaining balance = $10,000
Let's rearrange the equation:
Remaining balance = $75,000 - Selling price * 0.06 - $10,000
Now, substitute this equation back into equation 2 and solve for Selling price:
$75,000 - Selling price * 0.06 = $75,000 - Selling price * 0.06 - $10,000
The equation simplifies to:
$75,000 - Selling price * 0.06 = -$10,000
Add Selling price * 0.06 to both sides to isolate the Selling price:
$75,000 = Selling price * 0.06 + $10,000
Subtract $10,000 from both sides:
$65,000 = Selling price * 0.06
Divide both sides by 0.06 to solve for the Selling price:
Selling price = $65,000 / 0.06
Calculating this value will give us:
Selling price ≈ $1,083,333 (rounded to the nearest dollar)
Therefore, to net the owner $10,000 after paying the commission and the balance of his mortgage, the selling price should be approximately $1,083,333.
To determine the selling price required to net the owner $10,000, we need to calculate the commission and the remaining mortgage balance.
1. Commission:
- The owner agrees to pay a 6% commission.
- Multiply the commission rate by the selling price to calculate the commission amount.
Commission = 6% * Selling Price
2. Remaining Mortgage Balance:
- Subtract the mortgage balance from the selling price to determine the remaining amount after paying off the mortgage.
Remaining Balance = Selling Price - Mortgage Balance
3. Net Proceeds:
- Subtract the commission and the remaining mortgage balance from the selling price to determine the net proceeds.
Net Proceeds = Selling Price - Commission - Remaining Balance
4. Set up the equation to calculate the selling price:
Net Proceeds = $10,000
Selling Price - Commission - Remaining Balance = $10,000
Substitute the formulas for commission and remaining balance:
Selling Price - (6% * Selling Price) - $75,000 = $10,000
Now we can solve the equation for the selling price.
Let me calculate that for you.