A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 higher than in the first. The tax i

Question

A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 higher than in the first. The tax in the first city was 4% , and the tax in the second city was 3.5% . The total hotel tax paid for the two cities was $408.75. How much was the hotel charge in each city before tax?

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Thu Giang 5 years 2021-09-01T00:39:50+00:00 2 Answers 145 views 0

Answers ( )

  1. thanhha
    0
    2021-09-01T00:40:53+00:00
    Reply

    Answer:

    • $4750 and $6250

    Step-by-step explanation:

    Given

    • Hotel charge in city 1 = x
    • Hotel charge in city 2 = y

    The equation for the hotel charge:

    • y = x + 1500

    Taxes

    • Tax in the city 1 = 4% = 0.04x
    • Tax in the city 2 = 3.5% = 0.035y
    • Total tax = $408.75

    The equation for the tax:

    • 0.04x + 0.035y = 408.75

    Substitute y and solve for x:

    • 0.04x + 0.035(x + 1500) = 408.75
    • 0.04x + 0.035x + 52.5 = 408.75
    • 0.075x = 408.75 – 52.5
    • 0.075x = 356.25
    • x = 356.25/0.075
    • x = 4750

    Find the value of y:

    • y = 4750 + 1500
    • y = 6250

    The hotel charge was:

    • The first city: $4750
    • The second city: $6250
  2. Dau
    0
    2021-09-01T00:41:47+00:00
    Reply

    Sorry for the delay!

    Let x = charge before tax in 1st city, and y = charge before tax in 2nd city

    y = $1500 + x

    4/100x => tax in first city

    3.5/100y => tax in second city

    0.04x + 0.035y = $408.75

    We have the following system of equations to solve:

    \begin{bmatrix}y=1500+x\\ 0.04x+0.035y=408.75\end{bmatrix}\\\\\mathrm{Substitute\:}y=1500+x\\\\begin{bmatrix}0.04x+0.035\left(1500+x\right)=408.75\end{bmatrix}\\\begin{bmatrix}0.075x+52.5=408.75\end{bmatrix}\\\\\ x = 4750\\\mathrm{For\:}y=1500+x\\\mathrm{Substitute\:}x=4750:\\\\y=1500+4750 = 6250

    So the hotel charge before tax in city 1 = $4750, and the hotel charge before tax in city 2 = $6250

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