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 8%, and the tax in the second city was 8.5%. The total hotel tax paid for the two cities was $823.75. How much was the hotel charge in each city before tax?

Answer 1

Hotel charge in city 1= $5,250

Hotel charge in city 2= $4,750

Step-by-step explanation:

A theater group made an appearance in two cities.

Let x represent the amount charged in the first city

Let y represent the amount charged in the second city

The hotel charge before tax in the first city is $500 lower than the second city

y= x-500......equation 1

The tax in the first city is 8%

= 8/100

= 0.08

The tax in the second city is 8.5%

= 8.5/100

= 0.085

0.08x + 0.085y= 823.75.........equation 2

Substitute (x-500) for y in equation 2

0.08x + 0.085(x-500)= 823.75

0.08x + 0.085x - 42.5= 823.75

Collect the like terms

0.08x + 0.085x= 823.75+42.5

0.165x= 866.25

x= 866.25/0.165

x = 5,250

Substitute 5250 for x in equation 1

y= x-500

y= 5,250-500

y= 4,750

Hence the hotel charge in city 1 is $5,250 and the hotel charge in city 2 is $4,750