Question

David measured the heights of 10 of his classmates. He found the mean of their heights to be 54.8 inches. He then added in his own height and found the mean again. With David's height, the mean was 55 inches. What is David's height?​

Answer 1

Explanation:

Let David's height be x:

Sum of 10 classmates heights = 10 × 54.8 =548 inches.

Adding David's height = 548 + x

Average including David's height:

`(548+x)/(11) =55 \rightarrow 548+x=605 \rightarrow x=57`

David height is 57 inches.

Answer 2

Explanation:

Let's use "h" to represent David's height.

According to the problem, the mean height of David's 10 classmates is 54.8 inches:

(Height of Classmate 1 + Height of Classmate 2 + ... + Height of Classmate 10) / 10 = 54.8

We can simplify this equation to:

Height of Classmate 1 + Height of Classmate 2 + ... + Height of Classmate 10 = 548

When David's height is added to the group, the new mean height becomes 55 inches:

(Total Height of Classmates + David's Height) / 11 = 55

Substituting the first equation into the second equation:

(548 + h) / 11 = 55

Multiplying both sides by 11:

548 + h = 605

Subtracting 548 from both sides:

h = 57

Therefore, David's height is 57 inches.