SOLUTION: A hotel room bill for 5 nights was $706.25 including a 13% tax. What was the price before tax?

Hi, there--

Problem:
A hotel room bill for 5 nights was $706.25 including a 13% tax. What was the price before tax?

Solution:
We can solve this by working backwards. We know that the final cost of the room (after tax)
was $706.25. The tax rate is 13%, or 0.13 in decimal form.

Let's have x be the cost of the room for 5 nights before tax.

Let's map this out:
[the cost of the room (before tax)] + [13%] = [final cost]

In algebra, we have
x + 0.13x = 706.25

We solve for x to find the cost of the room. Combine like terms.
1.13x = 706.25

Divide both sides of the equation by 1.13.
x = 625

In the context of this problem x=625 means that the cost of the room for five days before tax 
is $625.00.

If you want the daily rate for the room, divide $625.00 by 5.
625.00/5 = 125

The daily rate for the room is $125.00

~Mrs.Figgy