What three numbers have an average of 86?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 86. This means if we add these three numbers together and divide by 3, we should get 86.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 86 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 86 * 3 = x + y + z
- So, the sum of our three numbers should be: 258
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 258.
Solution 1:
86, 86, 86
Verification:
(86 + 86 + 86) / 3 = 258 / 3 ≈ 86
This solution is correct!
Solution 2:
86, 86, 86
Verification:
(86 + 86 + 86) / 3 = 258 / 3 ≈ 86
This solution is correct!
Solution 3:
156, 37, 65
Verification:
(156 + 37 + 65) / 3 = 258 / 3 ≈ 86
This solution is correct!
Solution 4:
144, 14, 100
Verification:
(144 + 14 + 100) / 3 = 258 / 3 ≈ 86
This solution is correct!
Solution 5:
252, 4, 2
Verification:
(252 + 4 + 2) / 3 = 258 / 3 ≈ 86
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 258 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.