A seller you're working with still owes $[tex]50,000[/tex] on their mortgage but wants to net $[tex]20,000[/tex] after the mortgage and 7% commission are paid. What is the minimum for which the house must sell?
A. $[tex]75,269[/tex]
B. $[tex]79,645[/tex]
C. $[tex]89,900[/tex]
D. $[tex]90,645[/tex]
Answer (2)
Let x be the selling price.
Calculate the commission: 0.07 x .
Set up the equation: x − 0.07 x − 50000 = 20000 .
Solve for x : x = 0.93 70000 ≈ 75269 . The minimum selling price is 75 , 269 .
Explanation
Understanding the Problem Let's break down this problem. The seller wants to walk away with $20 , 000 after all expenses are paid. These expenses include paying off the remaining mortgage balance of $50 , 000 and a 7% commission on the sale price. Our goal is to find the minimum selling price that satisfies these conditions.
Defining the Variable and Commission Let x represent the minimum selling price of the house. The commission paid to the seller is 7% of the selling price, which can be written as 0.07 x .
Setting up the Equation The seller's net amount is the selling price minus the mortgage balance and the commission. So, we can write this as: x − 0.07 x − 50000
Formulating the Equation We know the seller wants to net $20 , 000 , so we set the expression equal to $20 , 000 : x − 0.07 x − 50000 = 20000
Simplifying the Equation Now, let's simplify and solve for x . First, combine the x terms: 0.93 x − 50000 = 20000
Isolating the Variable Term Next, add $50 , 000 to both sides of the equation: 0.93 x = 70000
Solving for x Finally, divide both sides by 0.93 to solve for x : x = 0.93 70000 ≈ 75268.82
Finding the Minimum Selling Price Therefore, the minimum selling price for the house must be approximately $75 , 268.82 . Since we are looking for the closest answer from the options, we can round it to $75 , 269 .
Examples
Imagine you're selling handmade jewelry. You need to cover the cost of materials (like beads and clasps) and also want to make a certain profit for your time and effort. This problem is similar: you need to figure out the selling price of your jewelry so that after covering the cost of materials and a percentage for your effort, you still reach your desired profit. This type of calculation is essential for any business to ensure profitability.
The minimum selling price for the house, after accounting for the mortgage and commission, must be approximately $75,269. Therefore, the correct option is (A) $75,269.
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