is pretty much the same as before, so without much fuss
a = charges before tax on first city
b = charges before tax on second city
how much is 3.5% of a? (3.5/100) * a, 0.035a.
how much is 7.5% of b? (7.5/100) * b, 0.075b.
the taxes for both cities, summed up to 347.50
so, 0.035a + 0.75b = 347.50
we also know that, whatever "a" may be, the second city charged $500 less, so b = a - 500.
[tex]\bf \begin{cases}
\boxed{b}=a-500\\
0.035a+0.075b=347.5\\
--------------\\
0.035a+0.075\left( \boxed{a-500} \right)=347.5
\end{cases}
\\\\\\
0.035a+0.075a-37.5=347.5\implies 0.110a=385
\\\\\\
a=\cfrac{385}{0.11}\implies a=3500[/tex]
how much did the second city charge? well, b = a - 500.
