What three numbers have an average of 590?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 590. This means if we add these three numbers together and divide by 3, we should get 590.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 590 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 590 * 3 = x + y + z
- So, the sum of our three numbers should be: 1770
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1770.
Solution 1:
590, 590, 590
Verification:
(590 + 590 + 590) / 3 = 1770 / 3 ≈ 590
This solution is correct!
Solution 2:
590, 590, 590
Verification:
(590 + 590 + 590) / 3 = 1770 / 3 ≈ 590
This solution is correct!
Solution 3:
1261, 463, 46
Verification:
(1261 + 463 + 46) / 3 = 1770 / 3 ≈ 590
This solution is correct!
Solution 4:
322, 155, 1293
Verification:
(322 + 155 + 1293) / 3 = 1770 / 3 ≈ 590
This solution is correct!
Solution 5:
1493, 23, 254
Verification:
(1493 + 23 + 254) / 3 = 1770 / 3 ≈ 590
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 1770 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.