Question

A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first the tax and the first city was 6% and the tax and the second city was 10% total hotel tax paid for two cities with $670 how much was the hotel charge in each city before tax

Answer 1

The hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.

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
`x.`

And the hotel charge in second city before tax be
`y.`

So, as the hotel charge of the second city was 1500 higher than the first.

Thus,

`y=x-1500` ........(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
`x` + 10% of
`y` = $670.

`(6x)/(100) +(10y)/(100) =670`

`0.06x+0.10y=670`

Substituting the value of
`y` from equation (1) we get:

`0.06x+0.10(x-1500)=670`

`0.06x+0.10x-150=670`

`0.16x-150=670`

Adding both sides by 150 we get:

`0.16x=820`

Dividing both sides by 0.16 we get:

`x=5125.`

The hotel charge in first city before tax = $5125.

Now, substituting the value of
`x` in equation (1) we get:

`y=x-1500`

`y=5125-1500`

`y=3625.`

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.