Question

Your take home pay is $1500 and you have 22% withheld in taxes. What is your gross pay?

Answer 1

We have been given that the take home pay is $1500 and 22% is withheld as taxes.

Let us assume that the gross pay is x dollars. Therefore, take home pay must be 78% of x because 22% of the pay is withheld as taxes, so you get to take home only 78% of the gross pay.

Since we have been given that take home pay is $1500 and it is 78% of the total gross pay. Therefore, we can set up an equation:

$78\%\text{ of }x=1500\\\frac{78}{100}x=1500\\0.78x=1500\\x=\frac{1500}{0.78}\\x=\ 1923.08$

Therefore, gross pay is $1923.08

Answer 2

The amount of gross pay is $\boxed{\ \ 1,923.07}$.

Further explanation:

The gross income is the total income that a person earn.

As per the government policy every person have to pay the taxes which is some percent of your gross income.

Therefore, the net income is the end result after various deductions of taxes from the gross income.

The gross income can be calculated as follows:

$\boxed{\text{Gross income}=\text{Net income}+\text{Taxes}}$    

The taxes are levied by the government on your gross income.

Therefore, the amount of taxes can be calculated as follows:

$\boxed{\text{Tax}=\dfrac{\text{Tax\%}}{100}\cdot \text{gross income}}$

Given:

The home pay as net income is $\ \ 1,500$ and the tax levied by the government is $22\%$.

Calculation:

Step 1:

Consider $x$ as the gross income in dollars.

The taxes imposed on income is $22\%$.

Use the formula of taxes to calculate the amount of tax paid.

$\begin{aligned}\text{Tax paid}&=\dfrac{22}{100}\cdot x\\&=0.22x\end{aligned}$  

Therefore, the amount of tax is $0.22x$.

Step 2:

Now, we have to calculate the value of gross pay.

The given net income is $\ \ 1,500$ and the amount of tax is $0.22x$.

Use the formula of gross income and substitute the value of net income and the amount of tax.

$\begin{aligned}\text{Gross income}&=\text{Net income}+\text{Taxes}\\x&=1500+0.22x\\x-0.22x&=1500\\0.78x&=1500\end{aligned}$    

Further solve the above equation to obtain the value of $x$.

$\begin{aligned}x&=\dfrac{1500}{0.78}\\&=\dfrac{1500}{78}\cdot 100\\&=1923.07\end{aligned}$

Therefore, the value of $x$ is as follows:

$\boxed{x=1923.07}$

Thus, the amount of gross pay is $\boxed{\ \ 1,923.07}$.

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Interest

Keywords:  Net value, gross value , home pay, gross pay, taxes, income, government, imposed, equations, linear equation, variable, real numbers, amount, value, formula.