Problem 56 - Elementary Algebra

Question

The annual take-home pay of a chemist is \(\$ 69,000\). Her monthly house payment is \(\$ 1255\). After making all of her house payments for the year, find the remaining amount of her annual take-home pay. Use a negative number to represent a house payment.

Step-by-Step Solution

Answer

Remaining annual take-home pay is \( \$ 53940 \).

Step 1: Determine Total Annual House Payments

First, calculate the total amount spent on house payments for the year. Multiply the monthly house payment \( \$ 1255 \) by 12 months:\[ \text{Total Annual House Payments} = 1255 \times 12 \] \[ = 15060 \]

Step 2: Calculate the Remaining Annual Take-Home Pay

Subtract the total annual house payments from the annual take-home pay. This will give the remaining annual take-home pay:\[ \text{Remaining Annual Take-Home Pay} = \$ 69000 - \$ 15060 \] \[ = \$ 53940 \]

Key Concepts

Annual Income

Understanding annual income is crucial for managing personal finances. Annual income is the total amount of money earned in a year before any deductions like taxes or expenses. For example, if a chemist has an annual take-home pay of \( \$ 69,000 \), this figure represents her total earnings after any necessary deductions, such as taxes, have already been taken out.
This income can come from various sources, such as a salary, bonuses, freelance work, or even investments. Knowing your annual income allows you to set a budget and plan for savings and expenses.

Monthly Expenses

Monthly expenses are recurring costs that one needs to pay every month. Common examples include rent or mortgage payments, utilities, groceries, and insurance. In the case of our exercise, the chemist has a monthly house payment of \( \$ 1255 \).
Calculating monthly expenses accurately is vital for budgeting. To find the total annual cost of a monthly expense, multiply the monthly amount by 12. For instance, the chemist’s yearly house payment would be \( 1255 \times 12 = 15060 \).
Tracking your monthly expenses helps in understanding your spending patterns and identifying areas where you can save money.

Subtraction of Large Numbers

When managing finances, you will often need to subtract large numbers. This exercise involves subtracting the total annual house payment from the annual income to find the remaining take-home pay. For the chemist:

• Annual take-home pay: \(\$ 69,000\)
• Total annual house payment: \( \$ 15,060 \)

Subtracting these results in the remaining annual take-home pay:
\(\$ 69,000 - \$ 15,060 = \$ 53,940 \).
This step demonstrates how understanding the subtraction of large numbers is essential in determining disposable income after covering significant expenses.

Basic Algebra Operations

Basic algebra operations, such as multiplication and subtraction, are essential skills for solving real-life financial problems. In this exercise, algebra helps calculate the chemist’s remaining annual take-home pay.
For instance, calculating the total annual house payment involved the multiplication step:
\( 1255 \times 12 = 15060 \).
Then, the subtraction operation was used to find out how much money remains after the payments:
\( \$ 69,000 - \$ 15,060 = \$ 53,940 \).
Mastering these basic algebra operations can be handy for making informed financial decisions and solving various mathematical problems encountered in everyday life.