A theater group made appearances in two cities. The hotel charge before tax in the second city was

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 6.5%, and the tax in the second city was 8%. The total hotel tax paid for the two cities was $351.25. How much was the hotel charge in each city before tax? 

Answer 1

We are given charge information before taxes and with taxes.  Let's establish some equations with variables.

 

Let x = the charge in the first city before tax

Let y = the charge in the second city before tax

 

 

Before Taxes

 

y = x - 1500           eq1

 

 

Taxes

 

0.065x + 0.08y = 321.25          eq2

 

 

We now have two equations with two variables to work with.  We want to be able to solve for one variable.  The best way to do this is to substitute one equation into another equation so that we only have to work with one equation with one variable. Let's substitute eq1 into eq2 since the variable y is defined by eq1.

 

 

0.065x + 0.08(x - 1500) = 351.25

 

Solve for x from this equation.  Once you solve for x, substitute the value of x into equation 1 to solve for y.  You will then have the charges of both cities.