Problem 2 - Elementary Algebra

Question

The rent on an apartment was increased from \(\$ 475\) a month to \(\$ 540\) a month. Find the amount that the rent was increased.

Step-by-Step Solution

Answer

The rent was increased by \(\$ 65\).

Step 1 - Identify initial and final rent

The initial rent is \(\$ 475\) per month and the final rent is \(\$ 540\) per month.

Step 2 - Calculate the increase in rent

Subtract the initial rent from the final rent:\[ \$ 540 - \$ 475 = \$ 65 \]

Step 3 - Interpret the result

The rent increased by \(\$ 65\) per month.

Key Concepts

headline of the respective core concept

Understanding how to calculate rent increase is very useful. Especially if you want to manage your finances better. This guide will walk you through 3 simple concepts to understand rent increases better. These include: finding the initial and final values, using subtraction to find the difference, and interpreting results accurately.

Initial and Final Values

First, identify the initial and final rent values. These values are crucial as they form the basis of your calculation. The initial value is the rent you were paying originally. In the example, the initial rent is \(\$475\) per month. The final value is the new rent you're expected to pay. In this case, it's \(\$540\) per month. Always double-check these values to avoid errors in your calculation. Having the correct initial and final values ensures that your subsequent calculations are accurate.

Subtraction

Once you have both the initial and final values, the next step is to subtract the initial value from the final value. Subtraction helps you determine the amount of increase. The formula is:
\[Final\ Rent - Initial\ Rent = Rent\ Increase.\]
For instance, in our case:
\(\$540 - \$475 = \$65.\)
So the rent increase is \(\$65\). Make sure you perform the subtraction carefully to avoid any mistakes. Even a small error can lead to incorrect results.

Interpreting Results

Finally, interpreting the results correctly is important. After subtracting, you know the exact amount of the increase. In our example, the rent increased by \(\$65\) per month.
Here’s how you can interpret it:

• The new rent is \(\$65\) more than the old rent.
• Budgeting: You need to adjust your monthly budget to account for an extra \(\$65\).
• Consider the percentage increase: For further insight, calculate the percentage increase. Use the formula:
  \[\left( \frac{Increase}{Initial\ Rent} \right) \times 100\]
  In this case, it would be \[\left( \frac{65}{475} \right) \times 100 = 13.68\%.\]
  Now you know that your rent increased by roughly 13.68%.

Understanding these results empowers you to make well-informed financial decisions.