the complete hotel bill was $68 (room and tax). If the sales tax is 9%, what was the cost for the room before the tax?

C - Cost of Hotel    r = Tax rate

 

 C + C r = C ( 1 +r) 

 

  C (1 + 0.09 ) = $68

 

  C = $68/1.09 = $62.39

Here is another approach with a lot of detail. 

 

Let x = cost of the room before taxes (since this is what we want to find, let it be x.  This is good practice for all word problems)

9% tax is equivalent to .09 (removing the percent sign and replacing with 9/100  because 9% = 9/100)

$tax = .09x

 

68 it total cost of the room plus total tax simply put:

 

$68 = $room + $tax (note that tax in this equation is the dollar amount, not the percentage of tax)

 

So that means

 

x+ (.09x) = 68  or  ( × + (9/100)x = 68)

 

1x+ .09x = 68

1.09x = 68  (divide both sides by 1.09)

 

x = 68/1.09

 

x = 62.385 (round to the nearest 100th because it's money. Money only goes out 2 decimal places.  So round UP because the last number is 5)

 

x = $62.39  FINAL ANSWER

 

check your work:

 

$tax = 62.39*.09 = 5.62

$room + $tax = $68

$62.39 + $5.62 = 68.01 (close enough.. because of rounding it's a little off... but still correct)

 

 

 

The reason Bam's answer is wrong is because the 9% is based off of the cost of the room BEFORE taxes.  This is a common mistake in calculating taxes.  Always remember that taxes are based off the ORIGINAL cost, not final.

 

Hope that helps.

Zakiyyah

room and tax minus tax = room before tax

 

$68 - 9% of $68 is the cost of the room before tax : that is $68 x (1 - 0.09) = $68 x (0.91) = $61.88

 

ATTENTION! PARVIZ'S ANSWER IS NOT CORRECT!