Problem 7 - Prealgebra

Question

In 2003 , the average U.S. household spent \(\$ 13,432\) on housing, \(\$ 2060\) on entertainment, \(\$ 5340\) on food, and \(\$ 7781\) on transportation. How much was spent on housing each month? Round to the nearest cent.

Step-by-Step Solution

Answer

Each month, \( \$1,119.33 \) was spent on housing.

Step 1: Identify Annual Housing Expenditure

The problem states that the average U.S. household spent \( \$13,432 \) annually on housing. This is the total amount spent over the course of a year.

Step 2: Calculate Monthly Housing Expenditure

To find out how much was spent each month, divide the annual expenditure by the number of months in a year. So, we calculate \( \frac{13,432}{12} \) which gives us \( 1,119.3333\ldots \) dollars per month.

Step 3: Round to the Nearest Cent

Since we have \( 1,119.3333\ldots \), we round this value to the nearest cent. This means we keep it to two decimal places, resulting in \( \$1,119.33 \).

Key Concepts

Annual Expenses

Annual expenses refer to the total amount of money spent over the course of one year. In this context, the focus is on specific categories such as housing, entertainment, food, and transportation expenses. Usually, annual expenses are calculated to give a comprehensive view of where money goes in a yearly budget. This helps in planning and managing household budgets effectively.

When considering annual expenses, it's crucial to recognize that these figures provide an overview, allowing individuals or families to anticipate and prepare for future financial needs. This preparation includes savings, investments, or adjustments in spending habits to meet future goals.

Understanding your annual expenses is the first step toward building a detailed budget that meets your financial objectives. It also gives you a clearer picture of where you might need to cut back or where you have room to spend more strategically in areas that matter most to you.

Division

Division is a fundamental mathematical operation used to break down a larger quantity into equal parts. In the context of expenses, division helps distribute annual costs evenly across multiple segments, like months or weeks. This operation is essential in determining consistent periodic expenses, such as the monthly housing costs in our exercise.

To perform division in our scenario, we take the total annual amount spent on housing and divide it by the number of months in a year, which is 12. The formula for this is simple:

• The annual expense amount (e.g., $13,432 for housing)
• Divided by the number of months in a year (12)

Mathematically, it is expressed as: \[ \text{Monthly Housing Expenditure} = \frac{\text{Annual Housing Expenditure}}{12} \] This calculation tells us exactly how much should be allocated for housing each month. Understanding division in this way helps manage budgets effectively and ensures that expenses are spread out evenly across time.

Rounding Numbers

Rounding numbers is a useful tool when you want to simplify figures to make them easier to handle and understand, particularly with monetary values. In financial contexts, such as determining monthly expenses, accuracy is typically maintained up to two decimal places, which represents cents.

When we say "rounding to the nearest cent," it means adjusting a number to ensure it has two numbers after the decimal point. If the digit in the thousandths place (third position after the decimal) is five or more, you increase the digit in the hundredths place by one. If it's less than five, the digit in the hundredths place stays the same.

Let's look at our exercise: the monthly housing cost calculation yields \(1,119.3333\ldots\). Here, you would examine the third digit after the decimal, which is 3. Since this is less than 5, we round down, making the monthly cost \(\$1,119.33\). Rounding correctly ensures precision in budgeting and financial reporting.