Help stuck on this

Question

A theater group made an appearance in two cities. The hotel charge before tax was in the second city was $500 higher than in the first. The tax in the first city was 9.5% and the tax in the second was 8.5%. The total hotel tax paid for the two cities was $942.50. How much was the hotel charge in each city before tax. 

Answer 1

First, read through a problem to get an idea of what's going on.

Then look for small pieces of the text that you can write expressions for.

Then figure out how to put them together.

We're only trying to write equation(s) at first.  Then you use your algebra skills to solve.

 

Let's call the before tax charges in the two cities A and B.

"The hotel charge before tax was in the second city was $500 higher than in the first."

We can write this as B = A + 500

 

We know the tax rate for each of the cities.  Since we have expressions for the basic charges, we can use them to calculate the two tax charges.

In city A, it's 0.095A.  In city B, it's 0.085B.

 

We know the total tax for both cities is 942.50.  That's just the sum of the two charges, so we now have two equations.

0.095A +0.085B = 942.50

 

Use that first equation from above to substitute for B in the second equation and solve for A.

B = A + 500

 

0.095A + 0.085(A+500) = 942.50

0.180A + 42.50 = 942.50

0.180A = 900

A = 5000

B = 5500