Problem 114 - Elementary Algebra

Question

In one month, the median home price in the Northeast rose from \(\$ 225,400\) to \(\$ 241,500\). Find the percent increase. (Round to the nearest tenth of a percent.

Step-by-Step Solution

Answer

The percent increase is 7.1\%.

Step 1: Identify the initial and final values

Determine the initial value, which is \(\$ 225,400\) and the final value, which is \(\$ 241,500\).

Step 2: Calculate the change in value

Subtract the initial value from the final value to find the change in price. \(\$ 241,500 - \$ 225,400 = \$ 16,100\).

Step 3: Calculate the percent increase

Use the formula for percent increase: \[ \text{Percent Increase} = \left( \frac{\text{Change in Price}}{\text{Initial Price}} \right) \times 100 \]. Substituting the values: \[ \text{Percent Increase} = \left( \frac{16,100}{225,400} \right) \times 100 = 7.1\% \].

Key Concepts

percent change

Understanding percent change is essential in many aspects of life, from personal finance to statistics. Percent change tells us how much something has increased or decreased in relation to its original value. The formula to calculate percent change is straightforward:
\[ \text{Percent Change} = \frac{\text{Change in Value}}{\text{Original Value}} \times 100 \]
This formula applies to both increases and decreases. To find the percent increase in median home prices, for instance, you simply substitute the values into the formula. It’s the exact method used in computing the 7.1% rise from \(225,400 to \)241,500.
Remember to always express your final answer with a % symbol. It’s also good practice to round your answers where necessary, especially if the question asks you to.

median home price

The median home price is a common metric in real estate that helps understand central market trends. The median is the middle value of an ordered list of numbers. For home prices, it means half the homes in the list cost less than the median and half cost more. This gives a better picture than the average because it isn’t skewed by extremely high or low prices.
In our exercise, the median home price increased from \(225,400 to \)241,500. Tracking these changes helps buyers, sellers, and economists understand market conditions. It’s also an essential figure for anyone looking into real estate investments or financial planning.

algebraic formulas

Algebraic formulas provide a systematic way to solve problems. A key formula in this exercise was the percent increase formula: \[ \text{Percent Increase} = \frac{\text{Change in Price}}{\text{Original Price}} \times 100 \]
Algebra makes problem-solving efficient and clear. By defining variables and creating equations, you can better understand relationships between numbers. For the home price example, we use the change in price (\(241,500 - \)225,400 = $16,100) and then apply the formula.
Understanding formulas and their applications lets you tackle similar problems in the future with confidence.

step-by-step problem solving

Step-by-step problem solving is a valuable skill. It breaks down complex problems into manageable pieces. Follow these essential steps:

• Identify the problem.
• Determine what you know and what you need to find out.
• Choose and apply the correct formula or method.
• Carry out the calculations step-by-step.
• Verify your answer.

In our exercise about median home prices, the steps included identifying initial and final values, calculating the price change, and then finding the percent increase. Always double-check calculations to avoid errors. Such a structured approach ensures clarity and accuracy in problem-solving tasks.