Problem 55 - Elementary Algebra

Question

The annual take-home pay of a teacher is \(\$ 34,000\). His monthly house payment is \(\$ 976\). After making all of his house payments for the year, find the remaining amount of his annual take-home pay. Use a negative number to represent a house payment.

Step-by-Step Solution

Answer

\( 22288 \)

Step 1: Determine Total House Payments for the Year

Calculate the annual house payment by multiplying the monthly house payment of \$976 by 12 months. \[ \text{Total House Payment} = 976 \times 12 = 11712 \]

Step 2: Subtract the Total House Payments from Annual Take-home Pay

Subtract the total annual house payment from the annual take-home pay: \[ 34000 - 11712 = 22288 \]

Key Concepts

Monthly Payments

Monthly payments refer to amounts that you regularly pay each month. These payments can be for rent, mortgages, utilities, and other recurring bills. Understanding how much you spend monthly helps manage your budget effectively. To find the yearly total of a monthly payment:

• Identify the monthly payment amount.
• Multiply it by 12 (the number of months in a year).

For example, if the monthly house payment is \(\$ 976\), you calculate the total yearly payments like this: \[ \text{Total House Payment} = 976 \times 12 = 11712 \]. This tells you how much you spend annually on your house payments.

Yearly Expenses

Yearly expenses are costs that accumulate over a year. These can include monthly payments and other periodic expenses. Understanding yearly expenses helps in budgeting and planning for savings or investments. To calculate yearly expenses:

• List all your monthly payments.
• Multiply each of these by 12.
• Add any additional yearly costs you might have.

For instance, if you have a monthly mortgage of \(\$ 976\) and an annual take-home pay of \(\$ 34,000\), then: \[ \text{Total House Payment} = 976 \times 12 = 11712 \] \[ \text{Remaining Take-home Pay} = 34000 - 11712 = 22288 \] This shows you the amount left after your house payments.

Subtraction in Algebra

Subtraction in algebra involves finding the difference between two numbers or expressions. It's essential for solving equations and understanding relationships between values. When dealing with subtraction:

• Identify the terms you need to subtract.
• Arrange them appropriately.
• Perform the subtraction operation.

For example, if you want to find the remaining annual take-home pay after house payments, you subtract the total yearly house payments from the annual salary: \[ \text{Remaining Pay} = 34000 - 11712 = 22288 \] Here, \(34000\) is the annual take-home pay and \(11712\) is the total yearly house payment. Subtraction gives the amount left for other expenses.