What three numbers have an average of 697?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 697. This means if we add these three numbers together and divide by 3, we should get 697.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 697 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 697 * 3 = x + y + z
- So, the sum of our three numbers should be: 2091
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2091.
Solution 1:
697, 697, 697
Verification:
(697 + 697 + 697) / 3 = 2091 / 3 ≈ 697
This solution is correct!
Solution 2:
697, 697, 697
Verification:
(697 + 697 + 697) / 3 = 2091 / 3 ≈ 697
This solution is correct!
Solution 3:
262, 1452, 377
Verification:
(262 + 1452 + 377) / 3 = 2091 / 3 ≈ 697
This solution is correct!
Solution 4:
1821, 163, 107
Verification:
(1821 + 163 + 107) / 3 = 2091 / 3 ≈ 697
This solution is correct!
Solution 5:
708, 1242, 141
Verification:
(708 + 1242 + 141) / 3 = 2091 / 3 ≈ 697
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 2091 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.