What three numbers have an average of 682?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 682. This means if we add these three numbers together and divide by 3, we should get 682.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 682 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 682 * 3 = x + y + z
- So, the sum of our three numbers should be: 2046
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2046.
Solution 1:
682, 682, 682
Verification:
(682 + 682 + 682) / 3 = 2046 / 3 ≈ 682
This solution is correct!
Solution 2:
682, 682, 682
Verification:
(682 + 682 + 682) / 3 = 2046 / 3 ≈ 682
This solution is correct!
Solution 3:
1057, 152, 837
Verification:
(1057 + 152 + 837) / 3 = 2046 / 3 ≈ 682
This solution is correct!
Solution 4:
1097, 753, 196
Verification:
(1097 + 753 + 196) / 3 = 2046 / 3 ≈ 682
This solution is correct!
Solution 5:
65, 1297, 684
Verification:
(65 + 1297 + 684) / 3 = 2046 / 3 ≈ 682
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 2046 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.