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ValentinkaMS [17]
3 years ago
11

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?
Mathematics
1 answer:
Radda [10]3 years ago
8 0
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.
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