Fifteen percent of an employee's taxable income is collected each paycheck. Before taxes are removed from each paycheck, $350 of tax-exempt expenses is taken out.
If the variable x represents the employee's pay before tax-exempt expenses and taxes are removed, which expression represents the employee's take-home pay after these deductions?
A. 0.15(x-350)
B. x-0.15-350
C. 0.85(x-350)
D. x-0.85-350
Answer (2)
Subtract the tax-exempt expenses from the gross pay: x − 350 .
Calculate the income tax deduction: 0.15 ( x − 350 ) .
Subtract the income tax deduction from the taxable income: ( x − 350 ) − 0.15 ( x − 350 ) .
Simplify the expression to find the take-home pay: 0.85 ( x − 350 ) . The final answer is 0.85 ( x − 350 ) .
Explanation
Understanding the Problem Let's break down how to calculate the employee's take-home pay. We need to consider the tax-exempt expenses and the income tax deductions.
Calculating Taxable Income First, we subtract the tax-exempt expenses from the employee's gross pay. This gives us the taxable income: x − 350 .
Calculating Income Tax Deduction Next, we calculate the amount of income tax that is deducted. This is 15% of the taxable income, which can be written as 0.15 ( x − 350 ) .
Calculating Take-Home Pay Finally, we subtract the income tax deduction from the taxable income to find the take-home pay: ( x − 350 ) − 0.15 ( x − 350 ) . We can simplify this expression by factoring out ( x − 350 ) : ( x − 350 ) ( 1 − 0.15 ) = ( x − 350 ) ( 0.85 ) = 0.85 ( x − 350 ) .
Final Answer Therefore, the expression that represents the employee's take-home pay after these deductions is 0.85 ( x − 350 ) .
Examples
Imagine you are managing your personal finances. You earn a certain amount each month, but before you receive your paycheck, some deductions are made for things like health insurance and taxes. This problem helps you calculate your actual take-home pay after these deductions. For example, if your gross pay is $2000 and your tax-exempt expenses are $350, then your take-home pay would be $0.85(2000 - 350) = 0.85(1650) = $1402.50. This calculation is crucial for budgeting and understanding your financial situation.
The expression representing the employee's take-home pay after deductions for tax-exempt expenses and taxes is 0.85 ( x − 350 ) . This accounts for the deduction of 15% income tax from the taxable income after subtracting $350. Therefore, the correct answer is option C: 0.85(x - 350).
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