18. the deductions from elis weekly net pay are federal income tax (fit) of $203, state income tax (sit) of…

18. the deductions from elis weekly net pay are federal income tax (fit) of $203, state income tax (sit) of 4.5% of gross, city income tax (cit) of 3.5% of gross, social security (ss) of 6.2% on first $97,500 and medicare of 1.45% of all income, $79 for health insurance, $5 for charity. his weekly net pay is $3,012.69. earnings to date are $10,510.20. find his weekly gross pay.\n\ntax deductions\tother deductions\ttotal deductions\nfit\tsit\tcit\tss\tmedicare\tmedical\tunion dues\tothers\n\nnotes: net pay = gross pay - total deductions

18. the deductions from elis weekly net pay are federal income tax (fit) of $203, state income tax (sit) of 4.5% of gross, city income tax (cit) of 3.5% of gross, social security (ss) of 6.2% on first $97,500 and medicare of 1.45% of all income, $79 for health insurance, $5 for charity. his weekly net pay is $3,012.69. earnings to date are $10,510.20. find his weekly gross pay.\n\ntax deductions\tother deductions\ttotal deductions\nfit\tsit\tcit\tss\tmedicare\tmedical\tunion dues\tothers\n\nnotes: net pay = gross pay - total deductions

Answer

Explanation:

Step1: Let the gross - pay be $x$.

The state income tax (SIT) is $0.045x$, the city income tax (CIT) is $0.035x$, the Social Security (SS) (since $10510.20<97500$, it's $0.062x$), the Medicare is $0.0145x$, the federal income tax (FIT) is $203$, health - insurance is $79$, and charity is $5$. The total deductions $D = 203+0.045x + 0.035x+0.062x + 0.0145x+79 + 5$. Simplify the total - deductions formula: $D=287+(0.045 + 0.035+0.062 + 0.0145)x=287 + 0.1565x$.

Step2: Use the net - pay formula.

We know that Net Pay = Gross Pay−Total Deductions. Given net pay is $3012.69$. So, $3012.69=x-(287 + 0.1565x)$. Expand the right - hand side: $3012.69=x - 287-0.1565x$. Combine like terms: $3012.69=(1 - 0.1565)x-287$. $3012.69 = 0.8435x-287$.

Step3: Solve for $x$.

Add $287$ to both sides of the equation: $3012.69 + 287=0.8435x$. $3299.69 = 0.8435x$. Divide both sides by $0.8435$: $x=\frac{3299.69}{0.8435}$. $x = 3912$.

Answer:

$3912$