Question

A theater group made appearances in two cities. The hotel charge before tax in the second city was
$1000
higher than in the first. The tax in the first city was
3%
, and the tax in the second city was
3.5%
. The total hotel tax paid for the two cities was
$360
. How much was the hotel charge in each city before tax?

Answer 1

@zepdrix help please

Answer 2

@fbi2015

Answer 3

sec thinking c:

Answer 4

thanks

Answer 5

@zepdrix Thanks so much.

Answer 6

Hmm this one is tricky :P nother sec lol

Answer 7

@zepdrix Ok.

Answer 8

Let's call the hotel charge BEFORE tax, \(\Large\rm H\).
So for the first hotel, maybe we'll call it \(\Large\rm H_1\),
and we'll call the other hotel \(\Large\rm H_2\).

The charge before tax in city two was 1000 more than in the first city.
So `hotel one` `plus` `1000` `is` `hotel two cost` before tax.\[\Large\rm H_1+1000=H_2\]

Answer 9

ok

Answer 10

This will help us later on ^ We don't need it right now.
I guess right now... we really just care about the tax values.
How is tax calculated? It's umm... we take a percentage of the total, and add it on top of the total, ya?

But if we're just looking at the tax, then we don't add it back to the total.
So the `tax` for `hotel one` will be 3.5% of H_1. (This will be multiplication).

Do you remember how to convert a percent to a decimal? :)

Answer 11

Yes

Answer 12

Woops I wrote that backwards :) The 3.5% is for hotel 2.

So the tax for hotel one will be \(\Large\rm 3\text{%}H_1\)
The tax for hotel two will be \(\Large\rm 3.5\text{%}\color{orangered}{H_2}\)

But we're going to use our information from before, to rewrite our H_2 in terms of H_1.
\[\Large\rm \color{orangered}{(H_1+1000)=H_2}\]
So our tax for hotel two will be \(\Large\rm 3.5\text{%}\color{orangered}{(H_1+1000)}\)

Then told us that the total tax of these two hotel rooms was 360.
So we'll add our taxes together and equate them to the total.\[\Large\rm 360=3\text{%}H_1+3.5\text{%}(H_1+1000)\]

Answer 13

We can use this equation to find the price of `hotel one before taxes`.
But we need to convert our percents to decimals or fractions first.
How do we change the 3% to a decimal? :)

Answer 14

ok

Answer 15

moviing the place of the decimal back

Answer 16

in this case

Answer 17

Mmm k good. We'll move the decimal 2 places to the left.\[\Large\rm 360=0.03H_1+0.035(H_1+1000)\]Let's distribute our 0.035 to each term in the brackets,\[\Large\rm 360=0.03H_1+0.035H_1+0.035\cdot1000\]\[\Large\rm 360=0.03H_1+0.035H_1+35\]Combine your like-terms (the H_1).\[\Large\rm 360=0.065H_1+35\]Then a few more steps to solve for H_1.

Answer 18

Are you inputting this into a website?
Or do you have multiple choice or something maybe? :)

I'm not totally confident on my steps here, so I just want to have a way to check our work.

Answer 19

ok.

Answer 20

What other steps should we do to solve for H_1?
We have 35 being `added`.
How can we "undo" the addition, what's the inverse operation that we can do?

Answer 21

subtract

Answer 22

its a two part question it asks for first city and second city

Answer 23

\[\Large\rm 325=0.065H_1\]Ok good.
We also have this number `multiplying` our H.
How can we undo that? :)

Answer 24

Keep in mind, after we find the price of hotel one,
hotel two is simply 1000 more than that.

Answer 25

ok

Answer 26

divide

Answer 27

Ok try that on a calculator real quick :)
I want you to do some of these steps too!
What do you get for the price of hotel one when you do the division?

Answer 28

5000

Answer 29

Ok great!
Hotel one cost, before taxes was 5000 dollars.
How much is hotel two cost?

Answer 30

6000

Answer 31

Ok good job \c:/

Answer 32

I Have two more similar

Answer 33

similar?! oh boy, these are not fun.
I don't know if I'm up for another haha.

Close this question since we've finished it.
Open a new one so it jumps to the top of the page.
Someone will probably come along to help, I'll try to stop by if I can find a moment c: