Including 5% sales tax, an inn charges $210.00 per night. Find the nightly cost at the inn before tax is added.

(a) Write an equation to model the problem. Let x represent the nightly cost before tax.

(b) Solve the equation to find nightly cost before tax. (Note: Your answer should be in the form $ddd.cc.)

1.05x = 210.00

x = 200.00

(a) The equation to model the problem is:

x + 0.05x = 210.00

(b) Solving the equation:
Combining like terms on the left side:
1.05x = 210.00

Dividing both sides by 1.05 to isolate the x variable:
x = 210.00 / 1.05

Evaluating the expression:
x ≈ $200.00

Therefore, the nightly cost at the inn before tax is added is approximately $200.00.

(a) To represent the problem mathematically, we can write the equation: x + 0.05x = $210.00. Here, x represents the nightly cost before tax, and 0.05x represents the 5% sales tax added to the nightly cost.

(b) To solve the equation and find the nightly cost before tax, we can simplify the equation by combining like terms:
1.05x = $210.00

Now, divide both sides of the equation by 1.05 to isolate x:
x = $210.00 / 1.05

Evaluating the right side of the equation, we get:
x ≈ $200.00

Therefore, the nightly cost at the inn before tax is added is approximately $200.00.