To determine the gross pay when given a take-home pay and a tax rate, we follow these steps:
1. Understand the Problem: We know that the take-home pay is what remains after tax has been deducted. Given that the take-home pay is $1,456 and 25% was withheld in taxes, we are to find the gross pay before tax deduction.
2. Formulate the Relationship:
- Let \( G \) be the gross pay.
- The tax rate is 25%, which is equivalent to \( 0.25 \).
3. Express the Take-Home Pay in Terms of Gross Pay:
The take-home pay is what remains after 25% of the gross pay has been deducted:
\( \text{Take-home pay} = G - G \times \text{tax rate} \)
This can be simplified to:
\( \text{Take-home pay} = G \times (1 - 0.25) \)
\( \text{Take-home pay} = G \times 0.75 \)
4. Solve for the Gross Pay:
We need to isolate \( G \) (the gross pay) in the equation:
\( 1456 = G \times 0.75 \)
To find \( G \), divide both sides by \( 0.75 \):
\( G = \frac{1456}{0.75} \)
5. Calculate the Gross Pay:
Perform the division:
\( G = 1941.33 \)
So, the gross pay, rounded to the nearest cent, is $1,941.33.
