Respuesta :
Answer:
The hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.
Step-by-step explanation:
Given:
A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first.
The tax of the first city was 6% and the tax of the second city was 10%.
Total hotel tax paid for two cities with $670.
Now, to find the hotel charge in each city before tax.
Let the hotel charge in first city before tax be [tex]x.[/tex]
And the hotel charge in second city before tax be [tex]y.[/tex]
So, as the hotel charge of the second city was 1500 higher than the first.
Thus,
[tex]y=x-1500[/tex] ........(1)
And as given, the tax of the first city was 6% and the tax of the second city was 10%, total hotel tax paid for two cities with $670.
6% of [tex]x[/tex] + 10% of [tex]y[/tex] = $670.
[tex]\frac{6x}{100} +\frac{10y}{100} =670[/tex]
[tex]0.06x+0.10y=670[/tex]
Substituting the value of [tex]y[/tex] from equation (1) we get:
[tex]0.06x+0.10(x-1500)=670[/tex]
[tex]0.06x+0.10x-150=670[/tex]
[tex]0.16x-150=670[/tex]
Adding both sides by 150 we get:
[tex]0.16x=820[/tex]
Dividing both sides by 0.16 we get:
[tex]x=5125.[/tex]
The hotel charge in first city before tax = $5125.
Now, substituting the value of [tex]x[/tex] in equation (1) we get:
[tex]y=x-1500[/tex]
[tex]y=5125-1500[/tex]
[tex]y=3625.[/tex]
The hotel charge in second city before tax = $3625.
Therefore, the hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.
