What three numbers have an average of 699?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 699. This means if we add these three numbers together and divide by 3, we should get 699.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 699 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 699 * 3 = x + y + z
- So, the sum of our three numbers should be: 2097
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2097.
Solution 1:
699, 699, 699
Verification:
(699 + 699 + 699) / 3 = 2097 / 3 ≈ 699
This solution is correct!
Solution 2:
699, 699, 699
Verification:
(699 + 699 + 699) / 3 = 2097 / 3 ≈ 699
This solution is correct!
Solution 3:
541, 1220, 336
Verification:
(541 + 1220 + 336) / 3 = 2097 / 3 ≈ 699
This solution is correct!
Solution 4:
902, 254, 941
Verification:
(902 + 254 + 941) / 3 = 2097 / 3 ≈ 699
This solution is correct!
Solution 5:
2, 233, 1862
Verification:
(2 + 233 + 1862) / 3 = 2097 / 3 ≈ 699
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 2097 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.