Alpturk wrote:An income tax is 20% in the lowest bracket of net income and 25% on net income in excess of that bracket. if the tax on $ 1800 of net income is $ 385.
what is the upper limit of the lowest bracket ?

Let x be the lower limit

Net Income .......... Tax
< x ................... 20%
> x ................... 25%

x/5 + (1800 - x)/4 = 385 --> x = $1300

sorry for poorly formatted table above. Does anyone know how to draw clean tables?

I'm having difficulty understanding this solution - is there an alternative approach to solving this problem?

You should consider x the upper limit of the lowest bracket.
Now, notice that 20% of 1800 is 360. Since the paid tax is 385 or greater than 360, this means that x is smaller than 1800.
So you get that:
up to x tax is 20%
whatever goes beyond x is taxed with 25% (in this case, what goes beyond x is 1800 - x).

Transform this into an equation and you get that:
total tax or 385 = 20%*x + 25%(1800 - x). This is equivalent to
385 = x/5 + 450 - x/4
385 = 450 - x/20
65 = x/20
x = 65*20 = 1300.