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Sagot :
Data:
City 1: A
City 2: B
Tax (r):
B= 7%
A=5%
[tex]\begin{gathered} A=C_A+C_A(0.05) \\ B=C_B+C_B(0.07) \end{gathered}[/tex]Cost without tax: C
Tax: C( r %)
The hotel charge before tax in the second city was $1500 lower than the first:
[tex]C_B=C_A-1500[/tex]The hotel tax paid for the two cities was $435:
[tex]C_A(0.05)+C_B(0.07)=435[/tex]Use the equations above to find the hotel charge (CA and CB) in each city:
1. Substitute in the second equation the CB for the value of CB in the first equation:
[tex]C_A(0.05)+(C_A-1500)(0.07)=435[/tex]2. Solve CA:
[tex]\begin{gathered} \text{0}.05C_A+0.07C_A-105=435 \\ \\ 0.12C_A-105=435 \\ \\ 0.12C_A=435+105 \\ \\ 0.12C_A=540 \\ \\ C_A=\frac{540}{0.12} \\ \\ C_A=4500 \end{gathered}[/tex]3. Use the value you find for CA to find CB:
[tex]\begin{gathered} C_B=C_A-1500 \\ C_B=4500-1500 \\ \\ C_B=3000 \end{gathered}[/tex]Then, the charge before tax of the hotel in first city (CA) is $4500 and in the second hotel (CB) is $3000
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