What three numbers have an average of 85?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 85. This means if we add these three numbers together and divide by 3, we should get 85.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 85 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 85 * 3 = x + y + z
- So, the sum of our three numbers should be: 255
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 255.
Solution 1:
85, 85, 85
Verification:
(85 + 85 + 85) / 3 = 255 / 3 ≈ 85
This solution is correct!
Solution 2:
85, 85, 85
Verification:
(85 + 85 + 85) / 3 = 255 / 3 ≈ 85
This solution is correct!
Solution 3:
212, 37, 6
Verification:
(212 + 37 + 6) / 3 = 255 / 3 ≈ 85
This solution is correct!
Solution 4:
229, 15, 11
Verification:
(229 + 15 + 11) / 3 = 255 / 3 ≈ 85
This solution is correct!
Solution 5:
221, 23, 11
Verification:
(221 + 23 + 11) / 3 = 255 / 3 ≈ 85
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 255 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.