Question

In a large housing complex, there are $15$small buildings and $22$ large buildings. Each of the large buildings has $10$ floors with $2$ apartments on each floor. Each of the small buildings has $12$floors with $3$apartments on each floor. How many apartments are there in all?

Answer 1

Step 1: Given data.

Number of large buildings $=22$

Number of small buildings$=15$

Number of floors in $1$ large building$=10$

Number of apartments on $1$ floor of large building$=2$

Number of floors in $1$ small building$=12$

Number of apartments on $1$ floor of small building$=3$

Step 2: Calculate the total number of apartments in a large building.

So, Total apartments in$1$ large building $=$Number of floors in $1$large building $\times$Number of apartments on $1$ floor of large building

$$\begin{gathered} =10\times 2 \\ =20 \end{gathered}$$

Step 3: Calculate the total number of apartments in a small building.

Total apartments in $1$small building $=$Number of floors in $1$ small building $\times$Number of apartments on $1$ floor of small building

$$\begin{gathered} =12\times 3 \\ =36 \end{gathered}$$

Step 4: Calculate the total number of apartments in entire housing complex.

Therefore, Total apartments in entire housing complex $=$ (Number of large buildings $\times$ Total apartment in$1$ large building ) $+$

(Number of small buildings $\times$ Total apartment in$1$small building )

$$\begin{gathered} =(22\times 20)+(15\times 36) \\ =440+540 \\ =980 \end{gathered}$$

Hence, there are $980$apartments in a large housing complex.