Question

A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 higher than in the first. The tax in the first city was 8%, and the tax in the second city was 5%. The total hotel tax paid for the two cities was $692.50. How much was the hotel charge in each city before tax?

Answer 1

Explanation:

x = hotel charge before tax in 1st city

y = hotel charge before tax in 2nd city

y = x + 1500

x×0.08 + y×0.05 = 692.5

why ?

a% of b = b×a/100

why ?

b = 100%

1% = 100%/100 = b/100

a% = a×1% = a×b/100 = b×a/100

so, e.g. 8% of something is that something multiplied by 8/100 or 0.08

now, we are using the first equation in the second equation :

x×0.08 + (x + 1500)×0.05 = 692.5

x×0.08 + x×0.05 + 1500×0.05 = 692.5

x×0.13 + 75 = 692.5

x×0.13 = 617.5

x = 617.5 / 0.13 = $4,750

y = x + 1500 = 4750 + 1500 = $6,250

the hotel charge before tax in the first city : $4,750

the hotel charge before tax in the second city : $6,250