To solve this problem, we need to understand how to calculate the employee's take-home pay after removing both tax-exempt expenses and taxes.
1. Identify the components:
- Employee's pay before tax-exempt expenses and taxes: [tex]\( x \)[/tex]
- Tax-exempt expenses: [tex]\( \$350 \)[/tex]
- Tax rate: [tex]\( 15\% \)[/tex] or [tex]\( 0.15 \)[/tex]
2. Calculate taxable income:
Tax-exempt expenses of [tex]\( \$350 \)[/tex] are deducted from the employee's pay [tex]\( x \)[/tex]. Hence, the taxable income is:
[tex]\[
x - 350
\][/tex]
3. Calculate the tax amount:
Taxes are collected at a rate of [tex]\( 15\% \)[/tex] on the taxable income. So the tax amount will be:
[tex]\[
0.15 \times (x - 350)
\][/tex]
4. Calculate the take-home pay:
The take-home pay is the employee's pay after deducting both the tax-exempt expenses and the tax amount. This can be expressed as:
[tex]\[
\text{Take-home pay} = \text{Taxable income} - \text{Tax amount}
\][/tex]
We have already found the taxable income to be [tex]\( x - 350 \)[/tex]. The tax amount is [tex]\( 0.15 \times (x - 350) \)[/tex].
Therefore, the take-home pay is:
[tex]\[
(x - 350) - 0.15 \times (x - 350)
\][/tex]
5. Simplify the expression:
Factor out [tex]\( x - 350 \)[/tex] from the terms:
[tex]\[
(x - 350) \left(1 - 0.15\right)
\][/tex]
Simplify the term inside the parentheses:
[tex]\[
(x - 350) \times 0.85
\][/tex]
Hence the expression for the take-home pay is:
[tex]\[
0.85(x - 350)
\][/tex]
Thus, the correct expression representing the employee's take-home pay after these deductions is:
[tex]\[
\boxed{0.85(x - 350)}
\][/tex]
