Question 1142571
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Let x = the hotel charge before tax in the first city;

    y = that of the second city.


Then from the condition you have these two equations in two unknowns


       x  -     y = 500     (1)

    0.08x + 0.04y = 640.    (2)


To solve the system of equations, use the Elimination method.


For it, from equation (1) express  x = 500 + y  and substitute it into the second equation. You will get


    0.08*(500+y) + 0.04y = 640.


Simplify and solve for y


    40 + 0.08y + 0.04y = 640

    0.12y = 640 - 40 = 600

    y = 600/0.12 = 5000.


<U>ANSWER</U>.  In the second city hotel charged $5000;  in the second city  $500 dollars more, or  5500  dollars.


<U>CHECK</U>.   0.08*5500 + 0.04*5000 = 640  dollars.    ! Correct !
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