What three numbers have an average of 550?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 550. This means if we add these three numbers together and divide by 3, we should get 550.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 550 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 550 * 3 = x + y + z
- So, the sum of our three numbers should be: 1650
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1650.
Solution 1:
550, 550, 550
Verification:
(550 + 550 + 550) / 3 = 1650 / 3 ≈ 550
This solution is correct!
Solution 2:
550, 550, 550
Verification:
(550 + 550 + 550) / 3 = 1650 / 3 ≈ 550
This solution is correct!
Solution 3:
1312, 133, 205
Verification:
(1312 + 133 + 205) / 3 = 1650 / 3 ≈ 550
This solution is correct!
Solution 4:
238, 55, 1357
Verification:
(238 + 55 + 1357) / 3 = 1650 / 3 ≈ 550
This solution is correct!
Solution 5:
1600, 1, 49
Verification:
(1600 + 1 + 49) / 3 = 1650 / 3 ≈ 550
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 1650 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.