Question

A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 lower than in the first. The tax in the first city was 3%, and the tax in the second city was 9% . The total hotel tax paid for the two cities was $495.How much was the hotel charge in each city before tax? Please help!!

Answer 1

@Talos could you help me with this one?

Answer 2

Yeah, we need to take it step by step

Answer 3

so x will be city 1

Answer 4

y will be city 2

Answer 5

first is the charge without tax so x=y+1500

Answer 6

and the taxes equation will be .03x+.09y=495

Answer 7

now substitute y=1500 for x in the second equation

Answer 8

.0.3x+0.9y(1500)=495

Answer 9

so now you have .03(y+1500) + .09y=495

Answer 10

no you are substituting it for x

Answer 11

because x=y+1500

Answer 12

ooh, sorry

Answer 13

Do you understand how I got there though?

Answer 14

Yes I do

Answer 15

ok now simplify for x

Answer 16

How do I do that? o., there is no x in the equation

Answer 17

Typo, I meant y

Answer 18

Sorry about that

Answer 19

are you gonna get 0.6y+1500=495?

Answer 20

@Talos

Answer 21

Not quite, do you know how the distributive property works?

Answer 22

Yes I do

Answer 23

Great! So distribute .03 over (y+1500)

Answer 24

.03y+45

Answer 25

yep now add .09y to that

Answer 26

45.09

Answer 27

or is it gonna be .03y+45+.09

Answer 28

nope, notice the y so it would be .12y+45=495

Answer 29

the y on .09y + .03y= .12y

Answer 30

oh okay, i understand how u get that

Answer 31

so now subtract 45 from both sides and get .12y=450

Answer 32

divide both sides by .12 and you get?

Answer 33

I got 3750

Answer 34

yep y=3750, going back to where we started we know y is Hotel 2, so now we need the rate for Hotel 1

Answer 35

use x=y+1500

Answer 36

plug in 3750 for y

Answer 37

x=3750+1500

Answer 38

so x=5250

Answer 39

SO your final answer is
Hotel 1's rate: $5250
Hotel 2's rate: $3750

Answer 40

Thanks very much :) I wrote tht all down incase I get another problem like that lol

Answer 41

No problem! With these types of problems, make two equations and substitute(: