What three numbers have an average of 267?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 267. This means if we add these three numbers together and divide by 3, we should get 267.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 267 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 267 * 3 = x + y + z
- So, the sum of our three numbers should be: 801
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 801.
Solution 1:
267, 267, 267
Verification:
(267 + 267 + 267) / 3 = 801 / 3 ≈ 267
This solution is correct!
Solution 2:
267, 267, 267
Verification:
(267 + 267 + 267) / 3 = 801 / 3 ≈ 267
This solution is correct!
Solution 3:
607, 128, 66
Verification:
(607 + 128 + 66) / 3 = 801 / 3 ≈ 267
This solution is correct!
Solution 4:
707, 91, 3
Verification:
(707 + 91 + 3) / 3 = 801 / 3 ≈ 267
This solution is correct!
Solution 5:
275, 3, 523
Verification:
(275 + 3 + 523) / 3 = 801 / 3 ≈ 267
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 801 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.