What three numbers have an average of 591?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 591. This means if we add these three numbers together and divide by 3, we should get 591.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 591 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 591 * 3 = x + y + z
- So, the sum of our three numbers should be: 1773
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1773.
Solution 1:
591, 591, 591
Verification:
(591 + 591 + 591) / 3 = 1773 / 3 ≈ 591
This solution is correct!
Solution 2:
591, 591, 591
Verification:
(591 + 591 + 591) / 3 = 1773 / 3 ≈ 591
This solution is correct!
Solution 3:
1149, 369, 255
Verification:
(1149 + 369 + 255) / 3 = 1773 / 3 ≈ 591
This solution is correct!
Solution 4:
1020, 147, 606
Verification:
(1020 + 147 + 606) / 3 = 1773 / 3 ≈ 591
This solution is correct!
Solution 5:
1736, 36, 1
Verification:
(1736 + 36 + 1) / 3 = 1773 / 3 ≈ 591
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 1773 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.