Question

Charlie , a frequent business traveler, is considering signing up for hotel reward program.Hotel Elegance is currently offering 50 points for signing up, plus 15 points for every night charlie books at the hotel. Alternatively , hotel Paradiso is offering a sign-up bonus of 250 points, plus 5 points per night. If charlie books a certain number of nights, points he earns the hotel will be the same. How many points will he have

Answer 1

350 points.

Explanation:

Given:

Charlie , a frequent business traveler, is considering signing up for hotel reward program.

Hotel Elegance is currently offering 50 points for signing up, plus 15 points for every night charlie books at the hotel.

Alternatively , hotel Paradiso is offering a sign-up bonus of 250 points, plus 5 points per night.

If charlie books a certain number of nights, points he earns the hotel will be the same.

Question asked:

How many points will he have ?

Solution:

Let Charlie books for number of nights =
`x`

Hotel Elegance is offering = 50 points for signing up + 15 points for every night

Total points, Charlie can earn from this hotel
`=50+15x`

Similarly, Charlie can earn from hotel Paradiso =
`250+5x`

As given, that for certain number of nights, points he earns the hotel will be the same. Hence, the equation will be:-

`50+15x=250+5x\\ \\ By\ subtracting \ both\ sides\ by\ 5x\ and\ 50\\ \\ 50-50+15x-5x=250-50+5x-5x\\ \\ 10x=200\\ \\ By \ dividing\ both\ sides\ by\ 10\\ \\ x=20`

By substituting the value:-

Charlie books for number of nights =
`x` = 20

You can take any one equation as both are equal.

Number of points, he will get
`=50+15x`

`=50+15*20\\ \\= 50+300\\ \\ =350`

Thus, he will have 350 points.