SOLUTION: Including 8% sales tax, a bed-and-breakfast inn charges $172.80 per night Find the inn's nightly cost before the tax is added. I tried and tried

Algebra ->  Linear-equations -> SOLUTION: Including 8% sales tax, a bed-and-breakfast inn charges $172.80 per night Find the inn's nightly cost before the tax is added. I tried and tried      Log On


   

Question 104691: Including 8% sales tax, a bed-and-breakfast inn charges $172.80 per night Find the inn's nightly cost before the tax is added.
I tried and tried
Found 2 solutions by Fombitz, mathnard:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's say the bed and breakfast charges X per night.
With 8% tax, it's $172.80.
Room Charge + Tax = Total
X+%2B+8X%2F100+=+172.80
X+%2B+.08X+=+172.80
1.08X+=+172.80
X+=+172.80%2F1.08
X+=+160.00
The room rate is $160.00 and the tax is ($160)(0.08) or $12.80.

Answer by mathnard(10) About Me  (Show Source):
You can put this solution on YOUR website!
Take a look at the problem. Doesn't the amount $172.80 includes 100% of the cost of a room, plus another 8% of the cost? This means that the $172.80 is actually 108% of the original cost. The word OF means multiply.

108% OF the original cost is equal to $172.80
* * * Remember that 108% means 108 out of 100 or 108%2F100 * * *
so %28108%2F100%29%2Ax=172.80



Now let's solve this equation.
%28108%2F100%29%2Ax=172.80

divide the 108 by 100 to get
1.08x=172.80

divide both sides by 1.08:
%281.08x%29%2F1.08=172.80%2F1.08

the 1.08s cancel on the left and we do the division on the right side leaving us with:
x=160

This means that the cost of a room at the bed and breakfast was $160.00 per night. Notice that 8% sales tax on this would be .08(160) or 12.80. What's 160+12.80? $172.80 or the total price!!!