What three numbers have an average of 698?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 698. This means if we add these three numbers together and divide by 3, we should get 698.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 698 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 698 * 3 = x + y + z
- So, the sum of our three numbers should be: 2094
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2094.
Solution 1:
698, 698, 698
Verification:
(698 + 698 + 698) / 3 = 2094 / 3 ≈ 698
This solution is correct!
Solution 2:
698, 698, 698
Verification:
(698 + 698 + 698) / 3 = 2094 / 3 ≈ 698
This solution is correct!
Solution 3:
1835, 53, 206
Verification:
(1835 + 53 + 206) / 3 = 2094 / 3 ≈ 698
This solution is correct!
Solution 4:
648, 860, 586
Verification:
(648 + 860 + 586) / 3 = 2094 / 3 ≈ 698
This solution is correct!
Solution 5:
182, 485, 1427
Verification:
(182 + 485 + 1427) / 3 = 2094 / 3 ≈ 698
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 2094 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.