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.