Certainly! Let's determine your gross pay given that your take-home pay is \[tex]$1500 and you have 22% withheld in taxes.
1. Define Take-Home Pay and Tax Withholding:
- Your take-home pay is \$[/tex]1500. This is the amount you receive after taxes have been withheld.
- 22% of your gross pay is withheld for taxes.
2. Express the Relationship Between Gross Pay and Take-Home Pay:
- Let [tex]\( G \)[/tex] be your gross pay.
- Take-home pay is calculated as the gross pay minus the withheld taxes.
- Since [tex]\( 22\% \)[/tex] is withheld, [tex]\( 78\% \)[/tex] of the gross pay is actually received as take-home pay.
3. Write the Equation for Take-Home Pay:
- The take-home pay (THP) can be represented as:
[tex]\[ \text{THP} = G \times (1 - 0.22) \][/tex]
- Therefore:
[tex]\[ 1500 = G \times 0.78 \][/tex]
4. Solve for Gross Pay (G):
- To get the gross pay, divide the take-home pay by 0.78:
[tex]\[ G = \frac{1500}{0.78} \][/tex]
5. Compute the Gross Pay:
- When you divide \[tex]$1500 by 0.78, you obtain:
\[ G = \frac{1500}{0.78} \approx 1923.08 \]
Therefore, your gross pay is approximately \$[/tex]1923.08.
