Respuesta :
Let's call the hotel charge in the first city as x. The tax in the first city was 3.5%, therefore, if we call the tax paid in the first city as t1, the tax paid is given by the following expression:
[tex]t_1=0.035x[/tex]The hotel charge before tax in the second city was $500 higher than in the first and the tax in the second city was 5.5%, therefore, if we call the tax paid in the second city as t2, the tax paid is given by the following expression:
[tex]t_2=0.055(x+500)=0.055x+27.5[/tex]If we multiply the first equation by 0.055/0.035, we're going to have
[tex]\begin{gathered} t_1\cdot\frac{0.055}{0.035}=0.035x\cdot\frac{0.055}{0.035} \\ \frac{11}{7}t_1=0.055x \end{gathered}[/tex]Then, if we subtract this expression from the expression for the tax on the second city, we're going to have
[tex]\begin{gathered} t_2-(\frac{11}{7}t_1)=0.055x+27.5-(0.055x) \\ t_2-\frac{11}{7}t_1=27.5 \end{gathered}[/tex]The total hotel tax paid for the two cities was $365. This gives to us another equation
[tex]t_1+t_2=365[/tex]If we subtract this equation from the previous expression, we're going to have a new equation only for the tax of the first city.
[tex]\begin{gathered} t_2-\frac{11}{7}t_1-(t_1+t_2)=27.5-(365) \\ t_2-\frac{11}{7}t_1-t_2-t_1=27.5-365 \\ -\frac{18}{7}t_1=-337.5 \\ t_1=\frac{7}{18}\cdot337.5 \\ t_1=131.25 \end{gathered}[/tex]Using this value on the first equation, we're able to determinate the value of x.
[tex]\begin{gathered} t_1=0.035x \\ (131.25)=0.035x \\ x=\frac{131.25}{0.035} \\ x=3750 \end{gathered}[/tex]The hotel charge on the first city before tax was $3750.00.
Since the hotel charge before tax in the second city was $500 higher than in the first, we have
[tex]x+500=3750+500=4250[/tex]The hotel charge on the second city before tax was $4250.00.
