Problem 3 - Elementary Algebra

Question

A contractor said that the cost to build a standard onestory home was about \(\$ 122\) per square foot. Find the cost to build a home with 1850 square feet.

Step-by-Step Solution

Answer

The cost to build the home is \(\text{\textdollar}225,700\).

Step 1: Understand the Given Data

The cost to build a standard one-story home is given as \(\text{\textdollar}122 \text{ per square foot}.\) We need to find the cost for a home that is 1850 square feet.

Step 2: Set Up the Equation

Multiply the cost per square foot by the total square feet to find the total cost. The equation is: \[ \text{Total Cost} = \text{Cost per square foot} \times \text{Total square feet} \]

Step 3: Perform the Calculation

Multiply \(122 \text{ per square foot} \times 1850 \text{ square feet} \). This will give you the total cost. \[ 122 \times 1850 = 225700 \]

Step 4: State the Final Answer

The total cost to build the home is \(\text{\textdollar}225,700\).

Key Concepts

Multiplication in Algebra

Multiplication is fundamental to algebra. When solving algebraic problems, you often need to multiply numbers and variables to find a solution. In our exercise, we multiplied the cost per square foot by the total square feet to find the total cost. Here's a quick breakdown:

• The phrase 'per square foot' indicates a rate, \(\text{\textdollar}122\), which is multiplied by a quantity, \(1850\) square feet.
• The multiplication tells us how much the entire quantity (house) will cost by multiplying the rate by the total.

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Understanding Cost Calculations

Cost calculations are essential in many real-world situations. For example, calculating the cost of building materials, labor, or whole construction tasks. Here's how you can approach it:
1. Identify the 'cost rate'—in your exercise, it's \(\text{\textdollar}122 \) per square foot.
2. Identify the total quantity—in our case, \(1850\) square feet.
3. Multiply these two numbers to get your total cost: \(122 \times 1850 = 225700\).
This step generally involves simple multiplication, but the key is accurately identifying the required rate and total quantity.

Building Construction Math

Math is indispensable in construction. Knowing how to correctly calculate costs ensures that projects are completed within budget. In this example:

• We needed to know the total area of the home: \(1850\) square feet.


• We also had to understand the cost per project unit—in this case, per square foot: \(\text{\textdollar}122\).
  Through multiplication, we arrived at the total cost: \(\text{\textdollar}225,700\).
  
  Math helps contractors accurately estimate costs and prevent overspending. If the costs are not calculated accurately, it can lead to financial losses.
  
  Understanding these basic mathematical principles is crucial in fields like construction. So, make sure to practice and master these calculations to excel in project planning and budgeting.