Question

The given dot plot shows the height of the buildings in a town. The height of 3 buildings are missing, but there is information using which we can calculate their heights.
1. The height of the third building is the mean height of the other two buildings.
2. If the height of the smallest building is $s$ ft, then the height of the tallest building is ($s$ + 30) ft.
3. The sum total of the heights = 2100 ft.

• A. 40 ft, 60 ft, 80 ft
• B. 45 ft, 60 ft, 75 ft
• C. 50 ft, 60 ft, 70 ft
• D. 30 ft, 60 ft, 90 ft

Answer 1

The correct option is B 45 ft, 60 ft, 75 ft

We can find the sum of the heights of the other buildings.
The total sum of the heights = 2100 ft
The sum of the heights given for the buildings = 25 + 25 + 35 + 35 + 40 + 50 + 50 + 50 + 50 + 50 + 60 + 75 + 75 + 75 + 75 + 90 + 90 + 90 + 90 + 90 + 100 + 100 + 100 + 100 + 100 + 100 + 100 = 1920 ft
Therefore, the sum of the missing three buildings = total height of the buildings – the sum of the heights given for the buildings
$=2100-1920=180$

$\text{Mean height of the tallest and smallest buildings}=\frac{s+s+30}{2}=\frac{2s+30}{2}=s+15ft$

So, the sum of the height of the three buildings = 𝑠 + (𝑠 + 15) + (𝑠 + 30)
𝑠 + (𝑠 + 15) + (𝑠 + 30) = 180
3𝑠 + 45 = 180
3𝑠 + 45 − 45 = 180 − 45
3𝑠 = 135

Dividing both the sides by 3,
$s=135÷3=45$ ft
So, the height of the three buildings will be 45 ft , 60 ft, and 75 ft, respectively.