Question

A hotel has a total of 315 rooms that come in two sizes: Single and Double. The hotel has 75 more single rooms as it does double rooms. How many of each type does the hotel have?

Answer 1

195 single rooms and 120 double rooms

Explanation:

Given

Represent the single room with S and the double with D.

`S = 75 + D` --- 75 more single rooms

`S + D = 315` --- Total number of rooms

Required

Find the number of each room

Substitute 75 + D for S in
`S + D = 315`

`75 + D + D = 315`

`75 + 2D = 315`

Collect Like Terms

`2D = 315 - 75`

`2D = 240`

Make D the subject

`D = (240)/(2)`

`D = 120`

Substitute 120 for D in
`S = 75 + D`

`S = 75 + 120`

`S = 195`