https://file.aiquickdraw.com/mathbot/file/1727364870013w3jl5w18.jpg

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

We know the following:

- The average of 29 numbers is 2586.
- The average of the first 14 numbers is 2589.
- The average of the last 14 numbers is 2584.

We need to find the 15th number.

### Step 1: Total Sum of All 29 Numbers
The average of the 29 numbers is 2586, so the total sum of these 29 numbers is:
\[
\text{Sum of all 29 numbers} = 29 \times 2586 = 75094
\]

### Step 2: Sum of the First 14 Numbers
The average of the first 14 numbers is 2589, so their total sum is:
\[
\text{Sum of the first 14 numbers} = 14 \times 2589 = 36246
\]

### Step 3: Sum of the Last 14 Numbers
The average of the last 14 numbers is 2584, so their total sum is:
\[
\text{Sum of the last 14 numbers} = 14 \times 2584 = 36176
\]

### Step 4: Find the 15th Number
The sum of the first 14 numbers and the last 14 numbers gives us the sum of 28 numbers. Subtracting this from the total sum will give us the 15th number:
\[
\text{15th number} = 75094 - (36246 + 36176) = 75094 - 72422 = 2672
\]

The 15th number is **2672**. Since this number is not one of the given options, the correct answer is:
\[
\boxed{(e) \text{None of these}}
\]

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Would you like further details on any part of this solution?

Here are 5 related questions:
1. How would the solution change if the 15th number was part of the first 14 or last 14 numbers?
2. Can you find the 16th number if the average of numbers from 1 to 16 was given?
3. How would you calculate the median if all numbers were available?
4. How can you check if all 29 numbers are equally spaced?
5. What happens to the total sum if the 15th number is increased by 10?

**Tip:** When calculating the total of a set of numbers based on the average, remember that multiplying the average by the count of numbers gives you the total sum directly.

Average of 29 numbers is 2586. The average of the first 14 numbers is 2589 and the average of the last 14 numbers is 2584. What is the 15th number?

In this problem, you are given the average of 29 numbers, the average of the first 14 numbers, and the average of the last 14 numbers. Learn how to find the 15th number using basic arithmetic and averages. Suitable for Grades 7-10.

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