A theater group made appearances in two cities. The hotel charge before tax in the second city was $1000 lower than in the first. The tax in the first city was 5.5% , and the tax in the second city was 5%. The total hotel tax paid for the two cities was $501.25 . How much was the hotel charge in each city before tax?
First City:
Second City:
x = first city
y = second city
y = x -1000 hotel charge is 100o less than the first city.
.055x +.05 y = 501.25
replace y in the second equation with x -1000 (You get this from the first equation)
.055x + .05(x -1000) = 501.25
Solve for x get the first city
use the first equation y = x -1000 to find the second city.
Be sure to check your final answers in both of the original equations to make sure you are correct.
x= 5500
y= 4000
Let's denote the hotel charge before tax in the first city as "x". Therefore, the hotel charge before tax in the second city would be "x - 1000".
Now, let's calculate the tax amount paid in the first city. The tax rate in the first city is 5.5%, so the tax amount paid in the first city would be 5.5% of x, which is 0.055x.
Similarly, the tax amount paid in the second city would be 5% of (x - 1000), which is 0.05(x - 1000).
The total hotel tax paid for the two cities was $501.25. Therefore, we can set up the equation:
0.055x + 0.05(x - 1000) = 501.25
Next, let's solve this equation step-by-step:
0.055x + 0.05x - 50 = 501.25 (Distribute 0.05 on the second term)
0.105x - 50 = 501.25 (Combine like terms)
0.105x = 551.25 (Add 50 to both sides)
x = 551.25 / 0.105 (Divide both sides by 0.105)
x ≈ $5250
Therefore, the hotel charge before tax in the first city is approximately $5250.
Substituting this value back into the equation for the hotel charge before tax in the second city:
x - 1000 = 5250 - 1000 = $4250
Therefore, the hotel charge before tax in the second city is $4250.
In summary,
Hotel charge before tax in the first city: $5250
Hotel charge before tax in the second city: $4250
To solve this problem, we can set up a system of equations. Let's call the hotel charge before tax in the first city "x" dollars. Since the hotel charge before tax in the second city is $1000 lower than in the first city, we can say that the hotel charge before tax in the second city is (x - 1000) dollars.
Now let's calculate the tax for each city. The tax in the first city is 5.5% of the hotel charge before tax, which is (0.055 * x). The tax in the second city is 5% of the hotel charge before tax, which is (0.05 * (x - 1000)).
According to the problem, the total hotel tax paid for the two cities is $501.25. So we can set up the equation:
0.055 * x + 0.05 * (x - 1000) = 501.25
Now we can solve this equation to find the value of x, which represents the hotel charge before tax in the first city.
0.055 * x + 0.05 * x - 50 = 501.25
0.105 * x - 50 = 501.25
0.105 * x = 551.25
x = 551.25 / 0.105
x ≈ 5250
So the hotel charge before tax in the first city is approximately $5250.
Substituting this value back into the equation, we can find the hotel charge before tax in the second city:
x - 1000 = 5250 - 1000 = 4250
So the hotel charge before tax in the second city is $4250.
Therefore, the hotel charge before tax in the first city is $5250 and in the second city is $4250.