Answer:
The hotel bill in the first city before tax would be $ 650
Step-by-step explanation:
Let x be the hotel charges ( in dollars ) before tax in the first city,
∵ Hotel charges before tax in the second city were $1500 lower than in the first.
So, the hotel charges in second city = ( x - 1500 ) dollars,
Now, percentage of tax in,
First city = 8%
Second city = 10%,
So, the total tax in both city = 8% of x + 10% of (x-1500)
![=\frac{8x}{100}+\frac{10(x-1500)}{100}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B8x%7D%7B100%7D%2B%5Cfrac%7B10%28x-1500%29%7D%7B100%7D)
![=0.8x + 0.10(x-1500)](https://tex.z-dn.net/?f=%3D0.8x%20%2B%200.10%28x-1500%29)
According to the question,
![0.8x + 0.10(x-1500)=435](https://tex.z-dn.net/?f=0.8x%20%2B%200.10%28x-1500%29%3D435)
![0.8x + 0.10x - 150 = 435](https://tex.z-dn.net/?f=0.8x%20%2B%200.10x%20-%20150%20%3D%20435)
![0.9x = 435 + 150](https://tex.z-dn.net/?f=0.9x%20%3D%20435%20%2B%20150)
![0.9x = 585](https://tex.z-dn.net/?f=0.9x%20%3D%20585)
![\implies x = \frac{585}{0.9}=650](https://tex.z-dn.net/?f=%5Cimplies%20x%20%3D%20%5Cfrac%7B585%7D%7B0.9%7D%3D650)
Hence, the hotel bill in the first city before tax would be $ 650.