Problem 30 - Elementary Algebra

Question

A condominium in south Boston has three bedrooms, two baths, and 1807 square feet of living area. The price of the condo is \(\$ 1,040,000\). Find the cost per square foot of this condo. Round to the nearest whole number.

Step-by-Step Solution

Answer

576

Step 1 - Identify Given Values

Identify the given values from the problem. The total price of the condo is \(\$ 1,040,000\) and the total living area is 1807 square feet.

Step 2 - Write the Formula

To find the cost per square foot, use the formula: \[ \text{Cost per square foot} = \frac{\text{Total Price}}{\text{Total Living Area}} \]

Step 3 - Substitute the Values

Substitute the given values into the formula: \[ \text{Cost per square foot} = \frac{1,040,000}{1807} \]

Step 4 - Perform the Division

Perform the division to find the cost per square foot: \[ \text{Cost per square foot} = 575.58 \]

Step 5 - Round to the Nearest Whole Number

Round the result to the nearest whole number: \[ \text{Cost per square foot} \approx 576 \]

Key Concepts

division

Division is a fundamental operation in math where you split a number into equal parts. In this exercise, we use division to find the cost per square foot of a condo.

We start with the total price of the condo, \(\$1,040,000\), and the total living area, \(1807 \) square feet. The division formula helps us divide the total price by the living area: \[ \text{Cost per square foot} = \frac{\text{Total Price}}{\text{Total Living Area}} \] This formula is essential because it allows you to evenly distribute the total cost over each square foot of the condo.

formula application

Applying a formula involves replacing variables with the actual numbers given in the problem. It simplifies finding the answer by giving us a clear path to follow.

First, we identify the variables from the problem:

• Total Price: \(\$1,040,000\)
• Total Living Area: \(1807 \) square feet

Next, we substitute these values into our formula: \[ \text{Cost per square foot} = \frac{1,040,000}{1807} \] This step is crucial as it allows us to proceed to the next step, which is performing the division to find the cost per square foot.

rounding numbers

Rounding numbers makes them easier to work with and understand, especially in practical scenarios. After performing division in the previous step, we got \(575.58\) as the cost per square foot.

However, it's often more practical to use whole numbers. To round \(575.58 \) to the nearest whole number, we look at the digit in the tenths place (which is \(5\)). If this digit is 5 or greater, we round up. If it is less than 5, we round down: \[ 575.58 \text{ rounded to the nearest whole number is } 576 \] Rounding helps us communicate the cost more clearly, avoiding unnecessary complexity in daily transactions.