Question

For Exercises \(1-20,\) solve.For Exercises \(1-20,\) solve. Lynn takes out a loan to buy a fixer-upper house. She then spends \(\$ 14,500\) in repairs and improvements. She sells the house for \(\$ 185,000 .\) If the payoff amount for the loan she took out to buy the house is \(\$ 151,728\) what is her net? Is it a profit or loss?

Short answer

Answer: Lynn made a profit of $18,772.

Step-by-step solution

1. Find the total cost of buying and fixing the house

Add the payoff amount for the loan to the cost of repairs and improvements. This will give us the total cost of buying and fixing the house: Total cost = Payoff amount for loan + Cost of repairs and improvements Total cost = \(151,728 + \)14,500$

2. Calculate the total cost

Now we need to calculate the total cost based on the given values: Total cost = \(151,728 + \)14,500 = \(166,228\)

3. Find the net

Subtract the total cost from the selling price to find the net: Net = Selling price - Total cost Net = \(185,000 - \)166,228$

4. Calculate the net

Now we need to calculate the net based on the given values: Net = \(185,000 - \)166,228 = \(18,772\)

5. Determine if it's a profit or loss

Since the net is positive, it means Lynn made a profit. So, her net is a profit of \(\$18,772\).

Key concepts

Basic Algebra

Understanding the basics of algebra is essential when dealing with math word problems involving calculations like profit or loss. Algebra provides a systematic method for solving equations and finding unknown values.

In the context of our exercise, algebra helps us combine different costs and revenues to determine the net outcome of a transaction. The equation used is a simple algebraic expression representing the total outcome: Total Outcome = Revenue - (Initial Cost + Additional Costs).

The numbers must be carefully substituted into the algebraic expression to solve for the unknown, which, in this case, is the net profit or loss. Each step follows basic principles of algebra, such as combining like terms (adding costs) and maintaining equalities (the selling price must balance against the total costs) to arrive at a solution. By mastering these basic algebraic skills, students become proficient at transforming real-world problems into solvable mathematical equations.

Profit and Loss

The concepts of profit and loss are crucial in both mathematics and real-world financial situations. A profit is earned when the selling price of an item is greater than the total cost of that item, including its purchase and any improvements made. Conversely, a loss occurs when the total cost surpasses the selling price.

In our textbook problem, Lynn's financial outcome from selling her house is determined by calculating her total costs (loan payoff plus repair costs) and subtracting this from the selling price of the house. The resulting figure is referred to as the 'net', which signifies the final financial gain or loss.

Remember, a positive net value indicates a profit, as evident in Lynn's scenario where she sold the house for more than the sum of her initial loan and the repair expenses. This straightforward approach allows students to apply basic mathematics to understand everyday financial transactions.

Math Word Problems

Math word problems can often seem daunting, but they are simply real-life scenarios presented in a narrative form requiring mathematical solutions. To tackle these effectively, comprehension is key—understanding the story and the question it's asking is crucial before jumping into calculations.

In the provided exercise, we analyzed a real-estate transaction to determine whether Lynn made a profit or incurred a loss on her house sale. We approached the problem step by step:

• First, we identified all the relevant financial figures provided in the problem.
• Next, we formulated an equation encapsulating the relationship between the costs and the selling price.
• We then performed the necessary arithmetic operations to calculate the total cost and the net value, which allowed us to conclude the profit or loss outcome.

Students can improve their problem-solving skills by regularly practicing different types of math word problems, gradually increasing the complexity as they become more confident with the foundational concepts.