Question

A total of 18816 tiles were used for decorating the rooms, kitchen, and bathrooms for all apartments in a building. Each apartment had 2 rooms, 1 kitchen, and 2 bathrooms. The number of tiles used is given below: 1 Kitchen=64 tiles; 1 Room=84 tiles and 1 Bathroom=52 tiles
How many apartments are there in the building?

Answer 1

Hint: In this problem, the given is a total number of tiles used to decorate rooms like kitchen and bathrooms for all apartments in a building and also in given how many tiles are used for kitchen, room, and bathroom respectively. We have to find the total number of apartments in the building. With the help of it, we will find the number of apartments in the building using the following formula.
* Number of apartments in the building is the division of the total number of tiles used for the building by the total number of tiles in an apartment.

Complete step by step solution:
 It is given that the total number of tiles used is\[18816\]
It is given that there are 2 rooms 1 kitchen and 2 bathrooms in one apartment and the tiles used for 1 Kitchen are 64 tiles, 1 Room is 84 tiles and 1 Bathroom is 52 tiles.
With this, we are going to find the number of tiles for one apartment.
Number of tiles used in 2 rooms is \[{\text{2}} \times {\text{84}} = 168\] tiles.
Number of tiles used in 1 kitchen is \[ = {\text{ }}64\] tiles.
Number of tiles used in 2 bathrooms is \[2 \times 52 = 104\] tiles.
Total number of tiles used for one apartment is \[{\text{168}} + {\text{64}} + {\text{1}}0{\text{4}} = {\text{336}}\] tiles.
Substituting the value of the total number of tiles used to decorate the apartments in the building and total number of tiles used for one apartment in the formula mentioned in the hint, we get,
Number of apartments in the building \[ = \dfrac{{18816}}{{336}} = 56\]

Hence there are 56 apartments in the building.

Note:
The number of tiles used in the apartment is found as the sum of the tiles used for decoration in every room. This is an important step in carrying forward the problem. Like problems are easy to understand but we have to think about what we have to find and what are the data’s in our hand. It will make the solution easiest for students.