Earlier quoted context omitted.
Would you be more sad if her salary went up to $15/hour (~2x), but yours went up to $210/hour (~3x, assuming you started from $70 ~= 10 x $7)? If this would not make you sad, then inequality isn't really the problem.
In terms of relative buying power, going from $7.50/h to $15/h is a much bigger jump than going from $70/h to $210/h. This is sort of a sick twist on the idea that "the house always wins" or "the market can remain illogical longer than you can remain solvent": at lower incomes, it sometimes only takes one car maintenance, one unexpected trip to the dentist, before you have to start picking and choosing what bills to…
Besides pay one of the largest burdens the poor face are all the government fees and indirect taxes that most of us don't notice in our daily lives. That twenty dollar tag fee renewal to me is nothing, but if you have to have a car and aren't clearing much twenty bucks can mean beans and rice.
Government already has the ability to track all fees paid it directly and can make assumptions about indirect fees so that the working poor; far different from the non working poor; can be relieved of some of the burden.
The only other option for solving inequality as many bemoan is to take from those earning so much so they really don't see the point and eventually everyone ends up poorer.