What three numbers have an average of 761?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 761. This means if we add these three numbers together and divide by 3, we should get 761.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 761 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 761 * 3 = x + y + z
- So, the sum of our three numbers should be: 2283
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2283.
Solution 1:
761, 761, 761
Verification:
(761 + 761 + 761) / 3 = 2283 / 3 ≈ 761
This solution is correct!
Solution 2:
761, 761, 761
Verification:
(761 + 761 + 761) / 3 = 2283 / 3 ≈ 761
This solution is correct!
Solution 3:
924, 1010, 349
Verification:
(924 + 1010 + 349) / 3 = 2283 / 3 ≈ 761
This solution is correct!
Solution 4:
1143, 91, 1049
Verification:
(1143 + 91 + 1049) / 3 = 2283 / 3 ≈ 761
This solution is correct!
Solution 5:
1909, 37, 337
Verification:
(1909 + 37 + 337) / 3 = 2283 / 3 ≈ 761
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 2283 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.