What three numbers have an average of 545?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 545. This means if we add these three numbers together and divide by 3, we should get 545.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 545 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 545 * 3 = x + y + z
- So, the sum of our three numbers should be: 1635
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1635.
Solution 1:
545, 545, 545
Verification:
(545 + 545 + 545) / 3 = 1635 / 3 ≈ 545
This solution is correct!
Solution 2:
545, 545, 545
Verification:
(545 + 545 + 545) / 3 = 1635 / 3 ≈ 545
This solution is correct!
Solution 3:
1436, 191, 8
Verification:
(1436 + 191 + 8) / 3 = 1635 / 3 ≈ 545
This solution is correct!
Solution 4:
57, 688, 890
Verification:
(57 + 688 + 890) / 3 = 1635 / 3 ≈ 545
This solution is correct!
Solution 5:
1326, 100, 209
Verification:
(1326 + 100 + 209) / 3 = 1635 / 3 ≈ 545
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 1635 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.