I'm really struggling with word problems. I don't know how to set this up.
2. You own a piece of land on which you owe the bank $12,760 to the bank. You decide to sell the land and want enough money to pay off the mortgage of the land. The real estate agent gets 6% of the selling price, and your city has a $400 real estate transfer tax paid by the seller. What should the range of the selling price be for you to get at least enough money to pay off your mortgage? Set up the inequality for this situation and then solve it. Your answer must be in inequality form.
You want the cash out after tax and commission to be at least $12,760.
Let X be the selling price.
Solve this inequality:
0.94 X -400 > 12,760
0.94 X > 13,160
X > $14,000
To solve this word problem, we need to figure out the range of the selling price for you to have enough money to pay off your mortgage.
Let's break down the information provided:
1. Mortgage amount owed: $12,760
2. Real estate agent's commission: 6% of the selling price
3. Real estate transfer tax: $400 paid by the seller
Now, let's start setting up the inequality to represent the situation:
Let "x" represent the selling price.
To calculate the real estate agent's commission, we need to multiply the selling price by 0.06 (which is the same as 6%). So, the real estate agent's commission can be represented as 0.06x.
The total cost associated with selling the land is the sum of the mortgage amount, the real estate agent's commission, and the real estate transfer tax. Therefore, the total cost can be expressed as:
Total Cost = Mortgage Amount + Real Estate Agent's Commission + Real Estate Transfer Tax
Substituting the values we have:
Total Cost = $12,760 + 0.06x + $400
To figure out the range of the selling price, we need to set up an inequality where the selling price (x) should result in a total cost greater than or equal to the mortgage amount owed. So, the inequality would look like:
Total Cost ≥ Mortgage Amount
$12,760 + 0.06x + $400 ≥ $12,760
Now that we have set up the inequality, you can solve it to find the range of the selling price (x) that would be sufficient to pay off the mortgage amount. To solve it, start by subtracting $12,760 from both sides of the inequality:
0.06x + $400 ≥ $12,760 - $12,760
Simplifying further:
0.06x + $400 ≥ 0
At this point, the inequality does not depend on the mortgage amount. Therefore, the range of the selling price (x) is such that the selling price needs to be greater than or equal to zero.
Thus, the inequality representing this situation is:
0.06x + $400 ≥ 0
To summarize, the range of the selling price (x) should be such that 0.06x (the real estate agent's commission) plus $400 (the real estate transfer tax) is greater than or equal to zero for you to have enough money to pay off your mortgage.