Which algebraic expression shows the average melting points of helium, hydrogen, and neon if [tex]\( h \)[/tex] represents the melting point of helium, [tex]\( j \)[/tex] represents the melting point of hydrogen, and [tex]\( k \)[/tex] represents the melting point of neon?

A. [tex]\( h + j + k \)[/tex]

B. [tex]\( h j k \)[/tex]

C. [tex]\( \frac{h + j + k}{3} \)[/tex]

D. [tex]\( \frac{h \pi}{3} \)[/tex]



Answer :

To determine the average melting point of helium, hydrogen, and neon, given their melting points as [tex]\( h \)[/tex], [tex]\( j \)[/tex], and [tex]\( k \)[/tex] respectively, we need to use the mathematical concept of finding the average of a set of numbers.

The average of a set of values is found by summing all the values present and then dividing that sum by the number of values.

Here’s a detailed step-by-step approach:

1. Identify the melting points:
- Helium: [tex]\( h \)[/tex]
- Hydrogen: [tex]\( j \)[/tex]
- Neon: [tex]\( k \)[/tex]

2. Sum the melting points:
To sum the melting points, we add them together:
[tex]\[ h + j + k \][/tex]

3. Count the number of elements:
There are three elements in this case - helium, hydrogen, and neon.

4. Divide by the number of elements:
To find the average, we divide the total sum by the number of elements:
[tex]\[ \frac{h + j + k}{3} \][/tex]

Now let’s look at the given options:
- Option A: [tex]\( h + j + k \)[/tex]
- This option gives the sum of the melting points but does not divide by the number of elements.
- Option B: [tex]\( h j k \)[/tex]
- This option suggests multiplying the melting points together, which is not the method for finding an average.
- Option C: [tex]\( \frac{h + j + k}{3} \)[/tex]
- This option correctly sums the melting points and then divides by 3, correctly calculating the average.
- Option D: [tex]\( \frac{h \pi}{3} \)[/tex]
- This option introduces [tex]\(\pi\)[/tex] (pi), which is irrelevant to calculating the average melting points of these elements.

Therefore, the correct algebraic expression to show the average melting points of helium, hydrogen, and neon is:

[tex]\[ \boxed{\frac{h + j + k}{3}} \][/tex]

The correct option is C.