A goldsmith has two alloys, the first containing $77\%$ and the second containing $96\%$. If $x$ grams of the first alloy are mixed with $y$ grams of the second, obtaining $100$ grams of an alloy which contains $85.93\%$ gold, find $x$ to the nearest gram.
$x=53,y=47$
I don't know where to begin at all.