Question

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 1

The answer is C because you have to subtract the x value from $350 and subtract 0.15 from 1.00!

Answer 2

Answer: C. 0.85(x-350)

Explanation:

Translate the rellevant information from the verbal statement into a meaningful algebraic expression:

1) x is the pay before tax-exempt expenses and taxes

2) $ 350 is exempt of taxes

3) Hence, the taxable income is x - 350

4) Fifteen percent of that is: (15/100) (x - 350)  = 0.15 (x - 350)

5) Therefore, the employee received  x - 350 - 0.15 (x - 350)

6) Now, you may manipulate the terms to obtain the desired expression:

• associative property of addition: (x - 350) - 0.15(x - 350)
• common factor: (x - 350) (1 - 0.15)
• do the operations: (x - 350)(0.85)
• commutative property: 0.85 (x - 350)

And that is the same expression of the third answer choice: C. 0.85(x-350)