What three numbers have an average of 518?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 518. This means if we add these three numbers together and divide by 3, we should get 518.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 518 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 518 * 3 = x + y + z
- So, the sum of our three numbers should be: 1554
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1554.
Solution 1:
518, 518, 518
Verification:
(518 + 518 + 518) / 3 = 1554 / 3 ≈ 518
This solution is correct!
Solution 2:
518, 518, 518
Verification:
(518 + 518 + 518) / 3 = 1554 / 3 ≈ 518
This solution is correct!
Solution 3:
141, 32, 1381
Verification:
(141 + 32 + 1381) / 3 = 1554 / 3 ≈ 518
This solution is correct!
Solution 4:
330, 563, 661
Verification:
(330 + 563 + 661) / 3 = 1554 / 3 ≈ 518
This solution is correct!
Solution 5:
407, 292, 855
Verification:
(407 + 292 + 855) / 3 = 1554 / 3 ≈ 518
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 1554 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.