What three numbers have an average of 710?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 710. This means if we add these three numbers together and divide by 3, we should get 710.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 710 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 710 * 3 = x + y + z
- So, the sum of our three numbers should be: 2130
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2130.
Solution 1:
710, 710, 710
Verification:
(710 + 710 + 710) / 3 = 2130 / 3 ≈ 710
This solution is correct!
Solution 2:
710, 710, 710
Verification:
(710 + 710 + 710) / 3 = 2130 / 3 ≈ 710
This solution is correct!
Solution 3:
2048, 28, 54
Verification:
(2048 + 28 + 54) / 3 = 2130 / 3 ≈ 710
This solution is correct!
Solution 4:
165, 362, 1603
Verification:
(165 + 362 + 1603) / 3 = 2130 / 3 ≈ 710
This solution is correct!
Solution 5:
2024, 63, 43
Verification:
(2024 + 63 + 43) / 3 = 2130 / 3 ≈ 710
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 2130 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.