This is a word problem and let's admit this that word problems are the most convoluted part of math because they apply our knowledge to real life.
Let's make this easy:
Step 1: List all the numerical info, ORGANIZE
*1st City (A):
Tax = 3%
*2nd City (B):
hotel charge (minus tax) = $500 less than A (note here is we get an equation; We have our left and right side)
Tax = 4.5%
Total tax for A and B = $258.75 (note here is where we get an equation; we have our left side and right side of equation)
Step 2: Put info from Step 1 into math terms
* Tax for A = 0.03A
* Tax for B = 0.045B
Hence: 0.03A + 0.045B = 258.75
Prior tax info (in orange before this) can be expressed as ---> B = A-500 (says that 2nd city before tax price is $500 less than first city)
Step 3: Solve the two equations you've come up with
0.03A + 0.045B = 258.75
B = A-500
* Isolate either A or B in first equation and substitute in second.
Ex) B = (258.75 - 0.03A)/0.045
(258.75 - 0.03A)/0.045 = A -500 (plug in B value to left side of 2nd eqn in place of A)
A = $3750 (remember that A and B represent hotel charge prior to tax)
B = (3750) - 500 (can substitute value A in either first or second eqn to get B)
B = $3250
Organization is key here. In problems where there are 2 variables (like A and B), find 2 equations and work with them like this.