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 4% , and the tax in the second city was 7% . The total hotel tax paid for the two cities was $455 . How much was the hotel charge in each city before tax?
Please help me follow the steps. I understand that you have to put the two cities in equations and solve but the numbers confuse me. the total of the two cities and the number earned.
first hotel charge ---- $x
2nd hotel charger ---- $x+1000
.04x + .07(x+1000) = 455
how about multiplying each term by 100 if you don't like decimals
4x + 7(x+1000) = 45500
11x + 7000 = 45500
11x = 38500
x = 3500
first hotel cost $3500
2nd hotel cost $4500
check:
.04(3500) + .07(4500) = 455
Well, let's break it down step by step, but don't worry, I'll try to make it as entertaining as possible!
Let's represent the hotel charge in the first city as 'x'. Since the tax in the first city is given as 4%, the tax paid in the first city would be 0.04x (tax rate times hotel charge).
Now, since the hotel charge in the second city was $1000 higher than in the first, we can represent it as 'x + $1000'. And the tax paid in the second city would be 0.07(x + $1000) (tax rate times hotel charge plus the $1000 difference).
Now, here comes the fun part! We know that the total hotel tax paid for the two cities was $455. So, we can set up an equation:
0.04x + 0.07(x + $1000) = $455
Now, let's simplify and solve this equation. First, let's distribute 0.07 to x and $1000:
0.04x + 0.07x + 0.07($1000) = $455
0.04x + 0.07x + $70 = $455
Now, let's combine like terms:
0.11x + $70 = $455
Next, let's isolate the x term by subtracting $70 from both sides:
0.11x = $455 - $70
0.11x = $385
Finally, divide both sides by 0.11 to solve for x:
x = $385 / 0.11
x ≈ $3500
So, the hotel charge before tax in the first city is approximately $3500.
Now, to find the hotel charge before tax in the second city, we can substitute this value back into the equation for the second city's hotel charge:
x + $1000 = $3500 + $1000 = $4500
Thus, the hotel charge before tax in the second city is $4500.
I hope these steps didn't leave you feeling too taxed! Let me know if you have any other questions!
Let's represent the hotel charge before tax in the first city as x.
According to the given information, the hotel charge before tax in the second city is $1000 higher than in the first city. Therefore, the hotel charge before tax in the second city can be represented as x + $1000.
Now, let's calculate the hotel tax for each city. In the first city, the tax is 4% of the hotel charge before tax, which is 0.04x. In the second city, the tax is 7% of the hotel charge before tax, which is 0.07(x + $1000).
The total hotel tax paid for the two cities is $455. So we can set up the equation:
0.04x + 0.07(x + $1000) = $455
Now, let's solve this equation step by step.
Step 1: Distribute the 0.07 inside the parentheses:
0.04x + 0.07x + 0.07($1000) = $455
Step 2: Simplify the expression:
0.04x + 0.07x + $70 = $455
Step 3: Combine like terms:
0.11x + $70 = $455
Step 4: Subtract $70 from both sides of the equation:
0.11x = $455 - $70
0.11x = $385
Step 5: Divide both sides of the equation by 0.11 to solve for x:
x = $385 / 0.11
x = $3500
So, the hotel charge before tax in the first city is $3500.
Now, let's find the hotel charge before tax in the second city:
x + $1000 = $3500 + $1000 = $4500
Therefore, the hotel charge before tax in the second city is $4500.
To solve this problem, let's break it down into steps:
Step 1: Assign variables to represent the unknowns.
Let's assume the hotel charge before tax in the first city is x dollars. As the charge in the second city is $1000 higher, we can represent it as (x + 1000) dollars.
Step 2: Calculate the tax amount for each city.
The tax in the first city is 4% of the hotel charge before tax. So, the tax in the first city can be represented as 0.04x dollars. The tax in the second city is 7% of the hotel charge before tax, which can be represented as 0.07(x + 1000) dollars.
Step 3: Write an equation for the total tax paid.
According to the problem, the total hotel tax paid for the two cities is $455. Thus, we can write the equation:
0.04x + 0.07(x + 1000) = 455
Step 4: Solve the equation.
To solve the equation, start by distributing 0.07 to x and 1000:
0.04x + 0.07x + 70 = 455
Combine like terms:
0.11x + 70 = 455
Subtract 70 from both sides of the equation:
0.11x = 385
Divide both sides of the equation by 0.11:
x = 3500
Step 5: Find the hotel charge in the second city.
Since the hotel charge before tax in the first city is $3500, the hotel charge in the second city (x + 1000) will be:
3500 + 1000 = $4500
So, the hotel charge before tax in the first city is $3500, and in the second city is $4500.