What three numbers have an average of 754?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 754. This means if we add these three numbers together and divide by 3, we should get 754.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 754 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 754 * 3 = x + y + z
- So, the sum of our three numbers should be: 2262
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2262.
Solution 1:
754, 754, 754
Verification:
(754 + 754 + 754) / 3 = 2262 / 3 ≈ 754
This solution is correct!
Solution 2:
754, 754, 754
Verification:
(754 + 754 + 754) / 3 = 2262 / 3 ≈ 754
This solution is correct!
Solution 3:
241, 560, 1461
Verification:
(241 + 560 + 1461) / 3 = 2262 / 3 ≈ 754
This solution is correct!
Solution 4:
1697, 452, 113
Verification:
(1697 + 452 + 113) / 3 = 2262 / 3 ≈ 754
This solution is correct!
Solution 5:
710, 416, 1136
Verification:
(710 + 416 + 1136) / 3 = 2262 / 3 ≈ 754
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 2262 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.