vladmire wrote:A certain state levies a 4 percent tax on the nightly rates of hotel rooms. A certain hotel in this state also charges a $2.00 nightly fee per room, which is not subject to tax. If the total charge for a room for one night was $74.80, what was the nightly rate of the room?

68
69
70
71
72

We can either do the algebra or backsolve using the choices.

Algebra:

Total cost = $2 + room charge + 4%(room charge)


74.80 = 2 + 1.04r
72.80 = 1.04r
72.80/1.04 = r
70 = r

[728/104 = 7]

Backsolve:

normally we start with (b) or (d), but (c) is just so much easier to work with, let's start there.

If r = 70, then total cost is 1.04(70) + 2 = 72.80 + 2 = 74.80

Yay! We get the right total cost, choose (C).

It should be C)

Let the nightly rate be R.

R + .04R + 2 = 74.80
1.04R = 72.80

R= 70

Check:

.04*70+70+2 = 74.80