SOLUTION: 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 6.5 %

Question 1112891: 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
6.5
%
, and the tax in the second city was
3.5
%
. The total hotel tax paid for the two cities was
$
427.50
. How much was the hotel charge in each city before tax?
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.

The system of 2 equations in 2 unknowns is THIS


     -x +      y = 1500,            (1)
 0.065x + 0.035y =  427.50.         (2)


To solve it, I will apply the  Elimination method.  For it, I will multiply eq(1) by 0.065, keeping the eq(2) as is.  You will get

-0.065x + 0.065y = 0.065*1500,       (1')
 0.065x + 0.035y =  427.50.          (2')


Next step is to add equations (1') and (2'). In this way, the terms with "x" will cancel each other, and you will get a single equation

for the unknown "y" only

0.065y + 0.035y = 0.065*1500 + 427.50,   or

0.1y = 525.


Hence,  y=  = 5250.


Answer.  In the second city, the theater paid $5250 before tax.


         In the first city, the theater paid 5250 - 1500 = 3750 dollars before tax.

Solved.

--------------
On the way, you learned on how the Elimination method works.

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