What three numbers have an average of 702?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 702. This means if we add these three numbers together and divide by 3, we should get 702.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 702 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 702 * 3 = x + y + z
- So, the sum of our three numbers should be: 2106
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2106.
Solution 1:
702, 702, 702
Verification:
(702 + 702 + 702) / 3 = 2106 / 3 ≈ 702
This solution is correct!
Solution 2:
702, 702, 702
Verification:
(702 + 702 + 702) / 3 = 2106 / 3 ≈ 702
This solution is correct!
Solution 3:
980, 120, 1006
Verification:
(980 + 120 + 1006) / 3 = 2106 / 3 ≈ 702
This solution is correct!
Solution 4:
1086, 46, 974
Verification:
(1086 + 46 + 974) / 3 = 2106 / 3 ≈ 702
This solution is correct!
Solution 5:
1290, 512, 304
Verification:
(1290 + 512 + 304) / 3 = 2106 / 3 ≈ 702
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 2106 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.