the mean kf three numbers is 17 23 and 2n. What is the sum of the digits of n

To solve this problem, let's break it down step by step.

### Step 1: The mean of three numbers
We are given the three numbers: \( 17 \), \( 23 \), and \( 2n \), and the mean is the average of these three numbers. The formula for the mean is:

\[
\text{Mean} = \frac{\text{sum of the numbers}}{3}
\]

Since the mean is the average of \( 17 \), \( 23 \), and \( 2n \), we have:

\[
\frac{17 + 23 + 2n}{3} = 17
\]

### Step 2: Simplifying the equation
First, calculate the sum of the known numbers \( 17 + 23 \):

\[
17 + 23 = 40
\]

Now, substitute this into the equation:

\[
\frac{40 + 2n}{3} = 17
\]

### Step 3: Solving for \( n \)
To solve for \( n \), first multiply both sides of the equation by 3 to eliminate the denominator:

\[
40 + 2n = 51
\]

Next, subtract 40 from both sides:

\[
2n = 11
\]

Now, divide by 2:

\[
n = \frac{11}{2} = 5.5
\]

### Step 4: Sum of the digits of \( n \)
Since \( n = 5.5 \), the sum of the digits of \( n \) is:

\[
5 + 5 = 10
\]

So, the sum of the digits of \( n \) is **10**.

Would you like further details or have any questions?

### Related Questions:
1. What would the mean be if \( n \) were a whole number instead?
2. How would the sum change if the mean was different, say 20?
3. Can you solve for \( n \) if one of the numbers was \( n + 3 \) instead of \( 2n \)?
4. What happens to the mean if we add another number to the list?
5. How can you express \( n \) as a fraction for other possible means?

### Tip:
Always check if the problem is asking for a sum of digits or a direct numerical value to avoid confusion!

The mean of three numbers is 17, 23, and 2n. What is the sum of the digits of n?

Learn how to find the sum of the digits of n when given the mean of three numbers (17, 23, and 2n). This step-by-step solution walks through using the mean formula to solve for n and calculate the sum of its digits. Suitable for students in Grades 6-8.

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