A fully-booked hotel has 62 guest in 35 rooms, some in single rooms, and some in double rooms. How many single and double rooms are there in the hotel? (It's with equations)

In this hotel there are 27 double rooms and 8 single rooms.

Step-by-step explanation:

We will consider the guests who stayed on double rooms as 'd' and the ones who stayed on single rooms as 's'. The sum of them should be the number of guests on the hotel. So we have:

s + d = 62

They need to be distributed in such a way that they'll fit in 35 rooms. The people who got on double rooms need to be divided by two, since two people will be on the same room. So we have:

s + d/2 = 35

Since we have two equations and two variables we can create a system of equations and solve it:

s+ d = 62

s + d/2 = 35

From the first equation we have:

s = 62 - d

Swaping this value on the second equation:

62 - d + d/2 = 35

62 -d/2 = 35

-d/2 = 35 - 62

-d/2 = -27

-d = -54

d = 54

Using that value we can solve for s:

s = 62 - 54 = 8

So they had 54 people staying on double rooms and 8 people staying on single rooms. Since 54 people stayed on double rooms there are 27 double rooms.