What three numbers have an average of 69?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 69. This means if we add these three numbers together and divide by 3, we should get 69.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 69 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 69 * 3 = x + y + z
- So, the sum of our three numbers should be: 207
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 207.
Solution 1:
69, 69, 69
Verification:
(69 + 69 + 69) / 3 = 207 / 3 ≈ 69
This solution is correct!
Solution 2:
69, 69, 69
Verification:
(69 + 69 + 69) / 3 = 207 / 3 ≈ 69
This solution is correct!
Solution 3:
64, 55, 88
Verification:
(64 + 55 + 88) / 3 = 207 / 3 ≈ 69
This solution is correct!
Solution 4:
146, 37, 24
Verification:
(146 + 37 + 24) / 3 = 207 / 3 ≈ 69
This solution is correct!
Solution 5:
130, 22, 55
Verification:
(130 + 22 + 55) / 3 = 207 / 3 ≈ 69
This solution is correct!
Explanation:
As you can see, there are many possible solutions. We can find more by:
- Choosing any two numbers
- Subtracting their sum from 207 to get the third number
Remember:
- The numbers don't have to be whole numbers.
- They can even be negative (although that might not make sense in some real-world contexts).
- The order of the numbers doesn't matter for the average.