The US taxation system appears to put earnings into bands.
Without access to the IRS taxation tables for the right tax year I can only suggest a way forward to answer this problem.
The percentage method appears to work by charging a percentage r% of the taxable weekly wage or salary and then adding on a fixed amount $f to give the tax withholding. We need to look at the band applicable to over $645 but under the next highest band. We also need the excess figure $E which reduces the tax liability.
The calculation goes like this: start with weekly salary W and find out which band it belongs to. Then subtract the excess E. We have W-E. Apply the tax rate of r%: (W-E)r/100 then add the fixed amount f: (W-E)r/100+f. This is the tax withholding. For this problem we have to work backwards: first locate the relevant band for >$645 to give us f, r% and E.
So we take $85.80 and subtract $f to give us 85.80-f dollars=(W-E)r/100. Next, we multiply by 100 to give us 100(85.80-f). This gives us (W-E)r. We divide by r next: 100(85.80-f)/r to get W-E. Finally we add E to get the weekly pay: 100(85.80-f)/r+E.
EXAMPLE
Let’s suppose r=12%, f=$18.30, E=$254.
100(85.80-18.30)/12+254=$816.50.
If you substitute values from tax tables for the relevant tax year you should be able to calculate the weekly pay.