What three numbers have an average of 587?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 587. This means if we add these three numbers together and divide by 3, we should get 587.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 587 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 587 * 3 = x + y + z
- So, the sum of our three numbers should be: 1761
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1761.
Solution 1:
587, 587, 587
Verification:
(587 + 587 + 587) / 3 = 1761 / 3 ≈ 587
This solution is correct!
Solution 2:
587, 587, 587
Verification:
(587 + 587 + 587) / 3 = 1761 / 3 ≈ 587
This solution is correct!
Solution 3:
174, 1059, 528
Verification:
(174 + 1059 + 528) / 3 = 1761 / 3 ≈ 587
This solution is correct!
Solution 4:
826, 448, 487
Verification:
(826 + 448 + 487) / 3 = 1761 / 3 ≈ 587
This solution is correct!
Solution 5:
75, 1446, 240
Verification:
(75 + 1446 + 240) / 3 = 1761 / 3 ≈ 587
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 1761 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.