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: 0.15 ( x − 350 ) .
Subtract the income tax from the taxable income: ( x − 350 ) − 0.15 ( x − 350 ) .
Simplify the expression to find the take-home pay: 0.85 ( x − 350 ) .
Explanation
Understanding the Problem Let's break down how to find the employee's take-home pay. We need to consider the tax-exempt expenses and the income tax.
Calculating Taxable Income First, the employee's pay before any deductions is represented by the variable x . From this, we subtract the tax-exempt expenses, which are $350 . This gives us the taxable income: x − 350 .
Calculating Income Tax Next, we calculate the amount collected for taxes. This is 15% of the taxable income, which is 0.15 ( x − 350 ) .
Calculating Take-Home Pay Finally, to find the take-home pay, we subtract the tax amount from the taxable income: ( x − 350 ) − 0.15 ( x − 350 ) . We can simplify this expression by factoring out ( x − 350 ) : ( x − 350 ) − 0.15 ( x − 350 ) = ( 1 − 0.15 ) ( x − 350 ) = 0.85 ( x − 350 ) .
Final Answer Therefore, the expression representing the employee's take-home pay is 0.85 ( x − 350 ) .
Examples
Imagine you work part-time and want to calculate your actual earnings after deductions. If your gross pay ( x ) is $1000 , and you have tax-exempt expenses like health insurance ( $350 ), your take-home pay is 0.85 × ( 1000 − 350 ) = 0.85 × 650 = $552.50 . This calculation helps you understand how much money you actually receive after taxes and other deductions, aiding in budgeting and financial planning.
The expression representing the employee's take-home pay after deductions is 0.85 ( x − 350 ) . This reflects the taxable income after subtracting the tax-exempt expenses and accounting for the income tax. The correct answer is option C.
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