Question

the surfside motel charges $128.50 per night plus a flat fee for parking of $27. the tropical winds motel charges $131.50 per night with no parking fee. (a) write the cost y to stay for x nights for each motel. assume that the patron needs parking. (b) find the number of nights for which the cost to stay at each motel would be the same. part 1 of 2 the cost to stay at the surfside motel is given by y = 128.5x + 27. the cost to stay at the tropical winds motel is given by y = 131.5x. part: 1 / 2 part 2 of 2 the cost to stay at each motel would be the same after nights.

Explanation:

Step1: Set the two cost - equations equal

Set $128.5x + 27=131.5x$.

Step2: Move the x - terms to one side

Subtract $128.5x$ from both sides: $27 = 131.5x-128.5x$.

Step3: Simplify the right - hand side

$131.5x - 128.5x=3x$, so $27 = 3x$.

Step4: Solve for x

Divide both sides by 3: $x=\frac{27}{3}=9$.

Answer:

9