What three numbers have an average of 971?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 971. This means if we add these three numbers together and divide by 3, we should get 971.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 971 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 971 * 3 = x + y + z
- So, the sum of our three numbers should be: 2913
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2913.
Solution 1:
971, 971, 971
Verification:
(971 + 971 + 971) / 3 = 2913 / 3 ≈ 971
This solution is correct!
Solution 2:
971, 971, 971
Verification:
(971 + 971 + 971) / 3 = 2913 / 3 ≈ 971
This solution is correct!
Solution 3:
2868, 12, 33
Verification:
(2868 + 12 + 33) / 3 = 2913 / 3 ≈ 971
This solution is correct!
Solution 4:
738, 1113, 1062
Verification:
(738 + 1113 + 1062) / 3 = 2913 / 3 ≈ 971
This solution is correct!
Solution 5:
315, 1110, 1488
Verification:
(315 + 1110 + 1488) / 3 = 2913 / 3 ≈ 971
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 2913 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.