What three numbers have an average of 746?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 746. This means if we add these three numbers together and divide by 3, we should get 746.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 746 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 746 * 3 = x + y + z
- So, the sum of our three numbers should be: 2238
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2238.
Solution 1:
746, 746, 746
Verification:
(746 + 746 + 746) / 3 = 2238 / 3 ≈ 746
This solution is correct!
Solution 2:
746, 746, 746
Verification:
(746 + 746 + 746) / 3 = 2238 / 3 ≈ 746
This solution is correct!
Solution 3:
1968, 114, 156
Verification:
(1968 + 114 + 156) / 3 = 2238 / 3 ≈ 746
This solution is correct!
Solution 4:
156, 1229, 853
Verification:
(156 + 1229 + 853) / 3 = 2238 / 3 ≈ 746
This solution is correct!
Solution 5:
1338, 309, 591
Verification:
(1338 + 309 + 591) / 3 = 2238 / 3 ≈ 746
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 2238 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.