To determine how many withholding allowances Mario currently claims, we'll follow a step-by-step approach using the given tax table and the information about his earnings and extra take-home pay.
### Step-by-Step Solution
1. Identify Mario's Current Earnings Range:
- Mario's gross biweekly earnings are [tex]\( \$784.21 \)[/tex].
- This falls within the range [tex]\( \$780 \leq \text{earnings} < \$800 \)[/tex].
2. Extract the Relevant Row from the Tax Table:
- For earnings of [tex]\( \$780 \)[/tex] to [tex]\( \$800 \)[/tex], the withholding amounts based on the number of allowances are:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
\text{At least} & \text{But less than} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10+ \\
\hline
780 & 800 & 89 & 71 & 53 & 34 & 20 & 7 & 0 & 0 & 0 & 0 & 0 \\
\hline
\end{array}
\][/tex]
3. Understand the Change in Withholding Amount:
- Mario claims one more withholding allowance which results in \[tex]$13 more in his take-home pay. This means the tax withheld decreases by \$[/tex]13.
4. Identify the Current Withholding Allowances:
- We need to find two consecutive columns where the difference in tax withheld is \[tex]$13.
Let's examine the differences:
- Difference between 34 (3 allowances) and 20 (4 allowances): \( 34 - 20 = 14 \)
- Difference between 20 (4 allowances) and 7 (5 allowances): \( 20 - 7 = 13 \)
Here, we find that the difference of \$[/tex]13 occurs between 20 (4 allowances) and 7 (5 allowances).
5. Conclusion:
- The change in tax implies Mario currently claims 4 withholding allowances (where the tax withheld is \[tex]$20).
- Claiming 1 more (i.e., moving to 5 allowances), the tax withheld becomes \$[/tex]7, providing an additional \$13 in take-home pay.
Therefore, Mario currently claims 4 withholding allowances.
Thus, the correct answer to the question is:
[tex]\[ \boxed{4} \][/tex]
