To determine how many withholding allowances Mario currently claims, we need to consider the given tax table and Mario's situation carefully. Mario has gross biweekly earnings of [tex]$784.21, which places him in the "780 & 800" wage range in our tax table.
Under this range, the tax data for different numbers of allowances is:
| Allowances | Tax Amount |
|------------|------------|
| 0 | $[/tex]89 |
| 1 | [tex]$71 |
| 2 | $[/tex]53 |
| 3 | [tex]$34 |
| 4 | $[/tex]20 |
| 5 | [tex]$7 |
| 6 | $[/tex]0 |
| 7+ | [tex]$0 |
Mario claims that by claiming 1 more withholding allowance, he would have $[/tex]13 more in his take-home pay, which means that the tax amount he currently pays will decrease by [tex]$13 if he claims one more allowance.
Upon examining the tax amounts for the "780 & 800" wage range for each allowance, we need to find a difference of $[/tex]13 between two adjacent tax amounts (i.e., between the tax for some number of allowances and the tax for one extra allowance):
- From [tex]$89 to $[/tex]71: Difference is [tex]$18
- From $[/tex]71 to [tex]$53: Difference is $[/tex]18
- From [tex]$53 to $[/tex]34: Difference is [tex]$19
- From $[/tex]34 to [tex]$20: Difference is $[/tex]14
- From [tex]$20 to $[/tex]7: Difference is [tex]$13
- From $[/tex]7 to [tex]$0: Difference is $[/tex]7
- From [tex]$0 to $[/tex]0: Difference is [tex]$0 (no drop because it's already 0)
The only pair that has a difference of exactly $[/tex]13 is between the tax amounts for 4 allowances and 5 allowances:
- [tex]$20 (4 allowances) - $[/tex]7 (5 allowances) = [tex]$13
This suggests Mario currently claims 4 allowances (because changing from 4 to 5 allowances results in precisely the $[/tex]13 reduction in tax, translating to $13 more in take-home pay).
Therefore, the number of withholding allowances Mario currently claims is:
[tex]\[
\boxed{4}
\][/tex]
