Problem 29 - Elementary Algebra

Question

A condominium in the East Village of New York City has two bedrooms, two bathrooms, and 1468 square feet of living area. The price of the condo is \(\$ 1,575,000\). Find the cost per square foot of this condo. Round to the nearest whole number.

Step-by-Step Solution

Answer

1073

Step 1 - Understand the problem

We need to find the cost per square foot of a condo given its total price and total living area in square feet.

Step 2 - Identify relevant information

The price of the condo is \( \$ 1,575,000\). The total living area is 1468 square feet.

Step 3 - Set up the formula

The formula to find the cost per square foot is given by \( \text{Cost per square foot} = \frac{\text{Total cost}}{\text{Total square feet}} \).

Step 4 - Substitute the values

Substitute \$ 1,575,000 for the total cost and 1468 for the total square feet into the formula: \[ \text{Cost per square foot} = \frac{1,575,000}{1468} \]

Step 5 - Calculate the division

Divide 1,575,000 by 1468: \[ \text{Cost per square foot} = 1073.224 \]

Step 6 - Round to the nearest whole number

Round 1073.224 to the nearest whole number to get the final answer: \[ 1073 \]

Key Concepts

Division

Division is a fundamental mathematical operation where you split a number into equal parts. In this problem, we needed to divide the total cost of the condo by the total square footage to find the cost per square foot. Think of it like splitting a pizza among friends. If you have a pizza that costs \(20 and want to divide it equally among 4 friends, each friend would pay \)5. Similarly, we wanted to find out how much each square foot 'pays' in terms of overall cost.

Rounding Numbers

Rounding numbers is important when you want to simplify a number while keeping its value close to the original. In our exercise, the calculated cost per square foot was 1073.224. To make it easier to understand, we rounded it to the nearest whole number. When rounding, we look at the digit right after the decimal point:

• If this digit is 5 or higher, we round up.
• If it's lower than 5, we round down.

In our case, since 224 (after the decimal) is less than 500, we rounded down to 1073.

Formula for Cost per Square Foot

A formula is a rule or principle expressed in algebraic symbols. To find the cost per square foot, we used a simple formula: \[ \text{Cost per square foot} = \frac{\text{Total cost}}{\text{Total square feet}} \] This means we're dividing the total price of the condo by the total area. The 'cost per square foot' is the price attributed to each individual square foot of space in the condo. It's a useful way to compare properties of different sizes and prices.

Practical Application of Algebra

Algebra isn't just abstract; it has practical uses in everyday life. In our example, we used algebra to calculate something very real—the price per square foot of a condo. This type of calculation helps in:

• Budgeting: Know if a property fits your budget
• Comparing properties: Understand which option offers better value
• Investment decisions: Determine potential returns and costs

By understanding and manipulating formulas, you can make informed decisions in real estate, finance, and other fields.