https://web2.0calc.com/api/ssl-img-proxy?src=%2Fimg%2Fupload%2F2bc35c167c283b602
Let x be the amount of income Joe would have to make for the 17% flat tax to equal the amount he pays in 2013.
17% of x = the amount he pays in 2013
the amount he pays in 2013 = 44,603.25 + 33% of (300,000 - 183,250)
the amount he pays in 2013 = 44,603.25 + 0.33 * (300,000 - 183,250)
the amount he pays in 2013 = 83,130.75
17% of x = 83,130.75
0.17x = 83,130.75
x = 83,130.75 / 0.17
x ≈ 489004.41
First, figure out how much tax would Joe pay using the "tax rates" in your table:
$44,603.25 + ($300,000 - 183,250) x 33% =
$44,603.25 + ($116,750 x 0.33) =
$44,603.25 + $38,527.50
=$83,130.75 - this is the income tax that Joe would pay using your table of tax rates.
$83,130.75 / 0.17 =$489,004.41 - this is the income that Joe would have to make for a flat rate of 17%.