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There are 18 floors in a building. Each floor has the same number of offices. Altogether there are 396

offices in the building. Write an equation to find f, the
number of offices in each floor of this building?
What is the value of f ?

3 answers

To find the number of offices on each floor (denoted as \( f \)), we can set up the equation based on the information given.

We know there are 18 floors and a total of 396 offices in the building. Therefore, we can express this relationship as:

\[ 18 \times f = 396 \]

To solve for \( f \), we can divide both sides of the equation by 18:

\[ f = \frac{396}{18} \]

Now, performing the division:

\[ f = 22 \]

So, the number of offices on each floor is \( f = 22 \).

how does it equal 22?

To see how \( f = 22 \) is calculated, let's break it down step-by-step:

  1. We start with the equation we set up: \[ 18 \times f = 396 \]

  2. To find \( f \), we rearrange the equation by dividing both sides by 18: \[ f = \frac{396}{18} \]

  3. Now we need to perform the division \( 396 \div 18 \).

  4. To simplify \( 396 \div 18 \):

    • First, we can simplify this by finding the greatest common divisor, but we can also do it directly.
    • If you calculate 396 divided by 18, you can do the division directly:
      • 18 goes into 39 two times (because \( 18 \times 2 = 36 \)), leaving a remainder of 3 (so we bring down the next digit to make it 36).
      • 18 goes into 36 exactly 2 times (because \( 18 \times 2 = 36 \)).

    So: \[ 396 \div 18 = 22 \]

This confirms that \( f = 22 \).

Thus, there are 22 offices on each floor.