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The ground floor of a tower has a very high ceiling, and the residential floors above it each have a constant, smaller, height.
The table compares the floor number and the height of its ceiling above the ground (in meters). The ground floor is floor 0 , and floors 1 and up are the residential floors.

Floor
Height (meters above ground)

8
31.6

15
54

22
76.4

What is the height of each residential floor?
meters

The ground floor of a tower has a very high ceiling, and the residential floors above it each have a constant, smaller, height. $\newline$ The table compares the floor number and the height of its ceiling above the ground (in meters). The ground floor is floor $0$ , and floors $1$ and up are the residential floors. $\newline$ \begin{tabular}{cc} $\newline$ Floor & Height (meters above ground) \\ $\newline$ \hline $8$ & $31$ . $6$ \\ $\newline$ $15$ & $54$ \\ $\newline$ $22$ & $76$ . $4$ $\newline$ \end{tabular} $\newline$ What is the height of each residential floor? $\newline$ meters

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Interpret the slope and y-intercept of a linear function

Full solution

Q. The ground floor of a tower has a very high ceiling, and the residential floors above it each have a constant, smaller, height.

\newline

The table compares the floor number and the height of its ceiling above the ground (in meters). The ground floor is floor

0

, and floors

1

and up are the residential floors.

\newline

\begin{tabular}{cc}

\newline

Floor & Height (meters above ground) \\

\newline

\hline

8

&

31

.

6

\\

\newline

15

&

54

\\

\newline

22

&

76

.

4

\newline

\end{tabular}

\newline

What is the height of each residential floor?

\newline

meters

Calculate Height Difference: First, we need to find the difference in height between two known floors to determine the height of a single residential floor. We can use the data for floors $8$ and $15$ for this calculation. $\newline$ Height of floor $15$ - Height of floor $8$ = Difference in height over $7$ floors. $\newline$ $54$ meters - $31.6$ meters = $22.4$ meters over $7$ floors.
Find Height per Floor: Next, we divide the difference in height by the number of floors to find the height of one residential floor. $\newline$ $22.4$ meters $\div$ $7$ floors = Height of one residential floor. $\newline$ $3.2$ meters per floor.
Verify Calculation with Another Set of Floors: To ensure there is no math error, we can check our calculation by using the height difference between floors $15$ and $22$ . $\newline$ Height of floor $22$ - Height of floor $15$ = Difference in height over $7$ floors. $\newline$ $76.4$ meters - $54$ meters = $22.4$ meters over $7$ floors.
Confirm Height per Floor: Again, we divide the difference in height by the number of floors to confirm the height of one residential floor. $\newline$ $22.4$ meters $\div$ $7$ floors = Height of one residential floor. $\newline$ $3.2$ meters per floor.

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