Answer:
Hotel charge in city 1= $5,250
Hotel charge in city 2= $4,750
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
