Question

Samuel, a frequent business traveler, is considering signing up for a hotel rewards program. Hotel Elegance is currently offering 727 points for signing up, plus 79 points for every night Samuel books at the hotel. Alternatively, Hotel Paradiso is offering a sign-up bonus of 985 points, plus 36 points per night. If Samuel 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?

Answer 1

After booking six nights, Samuel will earn the same amount of points from both Hotel Elegance and Hotel Paradiso, with a total of 1201 points.

Step-by-step explanation:

To determine after how many nights the total rewards points Samuel earns from both Hotel Elegance and Hotel Paradiso will be the same, we set up an equation where both hotel points equations are equal. Hotel Elegance gives 727 points for signing up plus 79 points per night, so its equation is 727 + 79n (where n is the number of nights). Hotel Paradiso offers 985 sign-up points plus 36 points per night, leading to 985 + 36n. By setting these equations equal to one another, we get 727 + 79n = 985 + 36n.

We can then solve for n by subtracting 727 and 36n from both sides, which gives us 43n = 258. When we divide both sides by 43, we find that n equals 6. Therefore, Samuel must book six nights to earn the same points from both hotels. To find out the total points, we insert n = 6 into either equation, for instance, 727 + 79(6) which gives us 1201 points.