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 tax-exempt expenses: Taxable income becomes x − 350 .
Calculate the tax amount: 0.15 ( x − 350 ) is deducted for taxes.
Determine take-home pay: Subtract the tax from taxable income: ( x − 350 ) − 0.15 ( x − 350 ) .
Simplify the expression: The final take-home pay is 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 initial pay. This gives us the taxable income: x − 350 .
Calculating Tax Amount Next, we calculate the amount collected for taxes, which is 15% of the taxable income. This is represented as 0.15 ( x − 350 ) .
Finding Take-Home Pay Now, we subtract the tax amount from the taxable income to find the take-home pay: ( x − 350 ) − 0.15 ( x − 350 ) .
Simplifying the Expression Finally, we simplify the expression to find the employee's take-home pay. We can factor out ( x − 350 ) from the expression: ( 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 monthly budget. You earn a certain amount, but before you can spend it, you have to account for tax-exempt expenses like health insurance and then calculate the income tax you owe. This problem demonstrates how to calculate your actual take-home pay after these deductions, helping you to plan your finances effectively. For instance, if your gross pay is $2000 and your tax-exempt expenses are $350, your take-home pay would be $0.85(2000 - 350) = 0.85(1650) = $1402.50.
The expression representing the employee's take-home pay after deductions is 0.85(x - 350). This is found by subtracting tax-exempt expenses from the pay and accounting for the 15% tax on the remaining amount. Hence, option C is the correct choice.
;
