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Let's go through the steps to determine the correct expression for the employee's take-home pay.
1. Define the variables:
- Let [tex]\( x \)[/tex] be the employee's pay before any deductions.
2. Subtract tax-exempt expenses:
- According to the problem, the employee has [tex]$\$[/tex]350[tex]$ of tax-exempt expenses that are taken out first. Thus, after the tax-exempt expenses are subtracted, the remaining amount is \( x - 350 \). 3. Calculate the tax: - The employee's taxable income is then \( x - 350 \). - The tax rate is 15%, which means that the tax amount is \( 0.15 \times (x - 350) \). 4. Subtract the tax from the taxable income: - After calculating the tax, we subtract this tax from the taxable income to find the take-home pay. - The take-home pay is given by \( (x - 350) - 0.15 \times (x - 350) \). Now, let's simplify this expression: \[ (x - 350) - 0.15(x - 350) \] Factor out \( x - 350 \) from both terms: \[ (x - 350)(1 - 0.15) \] Simplify the multiplication: \[ (x - 350) \times 0.85 \] This simplified expression represents the employee's take-home pay after the $[/tex]\[tex]$350$[/tex] of tax-exempt expenses and the 15% tax deduction.
Thus, the correct expression for the employee's take-home pay is:
[tex]\[ 0.85(x - 350) \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{0.85(x-350)} \][/tex]
1. Define the variables:
- Let [tex]\( x \)[/tex] be the employee's pay before any deductions.
2. Subtract tax-exempt expenses:
- According to the problem, the employee has [tex]$\$[/tex]350[tex]$ of tax-exempt expenses that are taken out first. Thus, after the tax-exempt expenses are subtracted, the remaining amount is \( x - 350 \). 3. Calculate the tax: - The employee's taxable income is then \( x - 350 \). - The tax rate is 15%, which means that the tax amount is \( 0.15 \times (x - 350) \). 4. Subtract the tax from the taxable income: - After calculating the tax, we subtract this tax from the taxable income to find the take-home pay. - The take-home pay is given by \( (x - 350) - 0.15 \times (x - 350) \). Now, let's simplify this expression: \[ (x - 350) - 0.15(x - 350) \] Factor out \( x - 350 \) from both terms: \[ (x - 350)(1 - 0.15) \] Simplify the multiplication: \[ (x - 350) \times 0.85 \] This simplified expression represents the employee's take-home pay after the $[/tex]\[tex]$350$[/tex] of tax-exempt expenses and the 15% tax deduction.
Thus, the correct expression for the employee's take-home pay is:
[tex]\[ 0.85(x - 350) \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{0.85(x-350)} \][/tex]
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