What three numbers have an average of 370?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 370. This means if we add these three numbers together and divide by 3, we should get 370.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 370 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 370 * 3 = x + y + z
- So, the sum of our three numbers should be: 1110
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1110.
Solution 1:
370, 370, 370
Verification:
(370 + 370 + 370) / 3 = 1110 / 3 ≈ 370
This solution is correct!
Solution 2:
370, 370, 370
Verification:
(370 + 370 + 370) / 3 = 1110 / 3 ≈ 370
This solution is correct!
Solution 3:
24, 203, 883
Verification:
(24 + 203 + 883) / 3 = 1110 / 3 ≈ 370
This solution is correct!
Solution 4:
749, 185, 176
Verification:
(749 + 185 + 176) / 3 = 1110 / 3 ≈ 370
This solution is correct!
Solution 5:
943, 66, 101
Verification:
(943 + 66 + 101) / 3 = 1110 / 3 ≈ 370
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 1110 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.