What three numbers have an average of 712?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 712. This means if we add these three numbers together and divide by 3, we should get 712.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 712 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 712 * 3 = x + y + z
- So, the sum of our three numbers should be: 2136
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2136.
Solution 1:
712, 712, 712
Verification:
(712 + 712 + 712) / 3 = 2136 / 3 ≈ 712
This solution is correct!
Solution 2:
712, 712, 712
Verification:
(712 + 712 + 712) / 3 = 2136 / 3 ≈ 712
This solution is correct!
Solution 3:
1309, 493, 334
Verification:
(1309 + 493 + 334) / 3 = 2136 / 3 ≈ 712
This solution is correct!
Solution 4:
436, 244, 1456
Verification:
(436 + 244 + 1456) / 3 = 2136 / 3 ≈ 712
This solution is correct!
Solution 5:
911, 362, 863
Verification:
(911 + 362 + 863) / 3 = 2136 / 3 ≈ 712
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 2136 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.