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A large housing complex has 30 towers. A...

A large housing complex has `30` towers. Among these six towers have `14` floors and `6` flats on each floor.
Twelve towers have `22` floor with 4 flats on each floor and `12` towers have `26` floors with `3` flats on each floor. Find the total number of flats in the housing complex.

A

`2,496` flats

B

`2,396` flats

C

`2,486` flats

D

`2,996` flats

Text Solution

AI Generated Solution

The correct Answer is:
To find the total number of flats in the housing complex, we will break down the problem step by step. ### Step 1: Calculate the number of flats in the first set of towers - There are **6 towers** with **14 floors** and **6 flats on each floor**. - First, calculate the total number of flats in one tower: \[ \text{Flats in one tower} = \text{Number of floors} \times \text{Flats per floor} = 14 \times 6 = 84 \text{ flats} \] - Now, calculate the total number of flats in 6 towers: \[ \text{Total flats in 6 towers} = 6 \times 84 = 504 \text{ flats} \] ### Step 2: Calculate the number of flats in the second set of towers - There are **12 towers** with **22 floors** and **4 flats on each floor**. - First, calculate the total number of flats in one tower: \[ \text{Flats in one tower} = 22 \times 4 = 88 \text{ flats} \] - Now, calculate the total number of flats in 12 towers: \[ \text{Total flats in 12 towers} = 12 \times 88 = 1056 \text{ flats} \] ### Step 3: Calculate the number of flats in the third set of towers - There are **12 towers** with **26 floors** and **3 flats on each floor**. - First, calculate the total number of flats in one tower: \[ \text{Flats in one tower} = 26 \times 3 = 78 \text{ flats} \] - Now, calculate the total number of flats in 12 towers: \[ \text{Total flats in 12 towers} = 12 \times 78 = 936 \text{ flats} \] ### Step 4: Calculate the total number of flats in the housing complex - Now, add the total number of flats from all three sets of towers: \[ \text{Total flats} = \text{Flats in 6 towers} + \text{Flats in 12 towers} + \text{Flats in 12 towers} \] \[ \text{Total flats} = 504 + 1056 + 936 \] \[ = 2496 \text{ flats} \] ### Final Answer The total number of flats in the housing complex is **2496 flats**. ---
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