Question

A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 lower than in the first. The tax in the first city was 3.5% , and the tax in the second city was 7.5% . The total hotel tax paid for the two cities was $347.50 . How much was the hotel charge in each city before tax?

Answer 1

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.

$\bf \begin{cases} \boxed{b}=a-500\\ 0.035a+0.075b=347.5\\ --------------\\ 0.035a+0.075\left( \boxed{a-500} \right)=347.5 \end{cases} \\\\\\ 0.035a+0.075a-37.5=347.5\implies 0.110a=385 \\\\\\ a=\cfrac{385}{0.11}\implies a=3500$

how much did the second city charge?  well, b = a - 500.