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 tax amount: 0.15 ( x − 350 ) .
Subtract the tax amount 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 calculate the employee's take-home pay step by step. We need to consider the tax-exempt expenses and the percentage taken out for taxes.
Calculating Taxable Income First, we subtract the tax-exempt expenses from the employee's gross pay. This gives us the taxable income. So, the taxable income is x − 350 .
Calculating Tax Amount Next, we calculate the amount that is collected for taxes. This is 15% of the taxable income, which is 0.15 ( x − 350 ) .
Calculating Take-Home Pay Now, we subtract the tax amount from the taxable income to find the take-home pay. This is ( x − 350 ) − 0.15 ( x − 350 ) .
Simplifying the Expression 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 representing the employee's take-home pay is 0.85 ( x − 350 ) .
Examples
Imagine you are earning money from a summer job. You get paid a certain amount, but before you receive your paycheck, some money is taken out for taxes and other expenses. This problem helps you understand how to calculate your actual take-home pay after these deductions. For example, if you earn $500 and have $100 in tax-exempt expenses and 10% is taken out for taxes, you can calculate your take-home pay using this method. This is useful for budgeting and understanding your finances.
To calculate the employee's take-home pay, first subtract the tax-exempt expenses from the gross pay to find taxable income. Then, calculate the tax amount as 15% of the taxable income and subtract it from the taxable income. The resulting expression for take-home pay is 0.85 ( x − 350 ) , so the correct answer is C.
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