Alec, a frequent business traveler, is considering signing up for a hotel rewards program. Hotel Elegance is currently offering 525 points for signing up, plus 35 points for every night Alec books at the hotel. Alternatively, Hotel Paradiso is offering a sign-up bonus of 402 points, plus 38 points per night. If Alec books a certain number of nights, the points he earns with either hotel will be the same. How many nights will that be? How many points will he have?

it will take 41 nights for the points he earns with either hotel to be the same.

Step-by-step explanation:

Let x represent the number of nights that it will take for the points he earns with either hotel will be the same.

Hotel Elegance is currently offering 525 points for signing up, plus 35 points for every night Alec books at the hotel. This means that the number of points that Alec will get of he spends x nights at the hotel is

35x + 525

Alternatively, Hotel Paradiso is offering a sign-up bonus of 402 points, plus 38 points per night. This means that the number of points that Alec will get of he spends x nights at the hotel is

38x + 402

For the points to be the same at either hotels, the number of nights would be

35x + 525 = 38x + 402

38x - 35x = 525 - 402

3x = 123

x = 123/3 = 41