Reggie S.
asked • 03/02/13A math word problem
A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 lower than in the first. The tax in the first city was 3%, and the tax in the second city was 4.5%. The total hotel tax paid for the two cities was $258.75. How much was the hotel charge in each city before tax?
More
2 Answers By Expert Tutors
The second hotel is $500 less than the first hotel:
Hotel1 = x
Hotel2 = x-500
Tax rates for each hotel:
Rate1 = .03
Rate2= .045
Solve for x:
Total Tax = Hotel1Rate1 + Hotel2Rate2
258.75 = (x)(.03) + (x-500)(.045)
258.75 = .03x +.045x - 22.5
281.25 = .075x
281.75/.075 = x
x=3750
Solution:
3750 = x = Hotel1
Hotel2 = x-500 = 3750 - 500 = 3250
Rizul N. answered • 03/02/13
Tutor
4.8
(12)
UNC-CH Grad For Math and Science Tutor
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
How?
* 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.
Still looking for help? Get the right answer, fast.
Ask a question for free
Get a free answer to a quick problem.
Most questions answered within 4 hours.
OR
Find an Online Tutor Now
Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.
Rizul N.
I am not sure why my explanation is not showing up but here is what I did:
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
How?
* 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.
03/02/13