Let's solve this problem step-by-step to determine the correct expression for the employee's take-home pay after the specified deductions:
1. Define the variables and understand the problem:
- Let [tex]\( x \)[/tex] represent the employee's pay before tax-exempt expenses and taxes are removed.
- [tex]\( \$350 \)[/tex] of tax-exempt expenses is taken out first.
- Fifteen percent (15%) of the remaining amount is collected as tax.
2. Calculate the remaining amount after tax-exempt expenses are removed:
- When [tex]\( \$350 \)[/tex] is taken out of [tex]\( x \)[/tex], the remaining amount is [tex]\( x - 350 \)[/tex].
3. Calculate the tax on this remaining amount:
- Fifteen percent (15%) of this remaining amount is collected as tax.
- The tax amount is: [tex]\( 0.15 \times (x - 350) \)[/tex].
4. Determine the take-home pay:
- The remaining amount after the tax-exempt expenses is [tex]\( x - 350 \)[/tex].
- After a 15% tax is taken from this amount, the take-home pay will be the remaining 85% of [tex]\( x - 350 \)[/tex] (since [tex]\( 100\% - 15\% = 85\% \)[/tex]).
- Therefore, the take-home pay is: [tex]\( 0.85 \times (x - 350) \)[/tex].
5. Find the correct expression in the given choices:
- The correct expression for the take-home pay after all deductions is [tex]\( 0.85(x - 350) \)[/tex].
Now, let's check the provided choices and see which one matches our derived expression:
- [tex]\( 0.15(x - 350) \)[/tex] - This represents the tax amount, not the take-home pay.
- [tex]\( x - 0.15 - 350 \)[/tex] - This expression is incorrect. It combines subtraction in an incorrect manner.
- [tex]\( 0.85(x - 350) \)[/tex] - This is the correct expression for the take-home pay.
- [tex]\( x - 0.85 - 350 \)[/tex] - This expression is also incorrect. It combines subtraction in an incorrect manner.
Thus, the correct answer is [tex]\( 0.85(x - 350) \)[/tex].
