Problem 56 - Prealgebra

Question

A cook making \(\$ 1,504.75\) a month has deductions of \(\$ 157.32\) for federal income tax, \(\$ 58.52\) for Social Security, and \(\$ 45.12\) for state income tax. How much does the cook take home after the deductions have been taken from his check?

Step-by-Step Solution

Answer

The cook takes home \( \$ 1,243.79 \) after deductions.

Step 1: Understand the Problem

The problem asks us to calculate the amount of money that the cook takes home after specific deductions from his monthly salary. We need to identify the salary and the deductions first.

Step 2: Identify the Given Values

The cook's monthly salary is \( \\( 1,504.75 \). The deductions are: \( \\) 157.32 \) for federal income tax, \( \\( 58.52 \) for Social Security, and \( \\) 45.12 \) for state income tax.

Step 3: Calculate the Total Deductions

Add the amounts of all the deductions to find the total deduction: \[ \\( 157.32 + \\) 58.52 + \\( 45.12 = \\) 260.96 \]

Step 4: Calculate the Take-Home Pay

Subtract the total deductions from the monthly salary to find the take-home pay: \[ \\( 1,504.75 - \\) 260.96 = \$ 1,243.79 \]

Step 5: Verify the Calculation

Ensure that each step was accurate by double-checking the arithmetic calculations. Adding the deductions again gives \( \\( 260.96 \). Subtracting from the salary, \( \\) 1,504.75 - \\( 260.96 \), confirms the take-home pay as \( \\) 1,243.79 \).

Key Concepts

Deductions Calculation

Deductions are amounts subtracted from a person's gross income before taxes, to determine their net income or take-home pay. Understanding deductions is critical in personal finance.
With deductions like federal income tax, Social Security, and state income tax, each is a set amount that reduces the salary. In our cook's case, we have:

• Federal income tax: \( \\(157.32 \)
• Social Security: \( \\)58.52 \)
• State income tax: \( \\(45.12 \)

These deductions reduce what the cook owes to government entities. To find the total deductions, you add up all individual deductions:\[\\)157.32 + \\(58.52 + \\)45.12 = \$260.96\]This total amount represents the total deductions from the monthly salary.

Monthly Income Calculation

The core task is finding out how much money the cook actually takes home every month after deductions. The starting point is the gross income, which is the total income before any deductions are taken.
For the cook, the gross monthly income is given as \( \\(1,504.75 \). To see what remains after subtracting deductions:

• Start with the gross monthly income: \( \\)1,504.75 \)
• Subtract the total deductions: \( \\(260.96 \)

The calculation of take-home pay is straightforward:\[\\)1,504.75 - \\(260.96 = \\)1,243.79\]This computation reveals the net income, or the amount actually received each month after deducting necessary costs. Knowing this helps manage finances effectively.

Personal Finance Math

Preparing an accurate monthly budget relies on understanding personal finance math. The practice involves calculating not just gross and net income, but also managing expenses and savings efficiently.
By understanding how deductions impact your take-home pay, you can better plan for everyday expenses such as rent, utilities, and groceries, while still setting aside money for savings or unforeseen expenses. Some important tips for handling personal finance include:

• Track monthly income and expenses to see where your money goes.
• Set a budget to ensure spending doesn't exceed income.
• Plan for taxes and deductions even if they vary monthly.
• Save consistently, even a small percentage, for future stability.

Mastering personal finance starts with understanding these basic arithmetic calculations. This foundation can lead to better financial decision-making in the long term.