# Question #c856b

Apr 16, 2017

There are 16 windows on the first floor.

#### Explanation:

Let $x$ equal the number of windows on the second floor.

Thus, the number of windows on the first floor is equal to $x - 2$, and the number of windows on the third floor is $\frac{x}{2}$.

Given that there are 9 windows on the third floor, we set $\frac{x}{2}$ equal to 9 and find that:
$\frac{x}{2} = 9$
$x = 18$

There are thus 18 windows on the second floor, but there are two fewer on the first floor. Therefore the first floor has 16 windows.

Apr 16, 2017

$16$ windows on the first floor.

#### Explanation:

We have to define a variable first to be able to make an equation.

The first floor has the smallest number of windows, so,
let the number of first floor windows be $x$.

Write the windows on the other floors in terms of $x$

The second floor has two more: $\text{ } \therefore x + 2$ windows

The third floor has half as many as the second floor:

The number of windows on the the third floor = $\frac{x + 2}{2}$

But there are $9$ windows on the third floor.
$\therefore \frac{x + 2}{2} = 9 \text{ } \leftarrow$ solve for x

$x + 2 = 2 \times 9$

$x = 18 - 2$

$x = 16$

$16$ windows on the first floor.