What three numbers have an average of 374?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 374. This means if we add these three numbers together and divide by 3, we should get 374.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 374 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 374 * 3 = x + y + z
- So, the sum of our three numbers should be: 1122
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1122.
Solution 1:
374, 374, 374
Verification:
(374 + 374 + 374) / 3 = 1122 / 3 ≈ 374
This solution is correct!
Solution 2:
374, 374, 374
Verification:
(374 + 374 + 374) / 3 = 1122 / 3 ≈ 374
This solution is correct!
Solution 3:
639, 401, 82
Verification:
(639 + 401 + 82) / 3 = 1122 / 3 ≈ 374
This solution is correct!
Solution 4:
654, 167, 301
Verification:
(654 + 167 + 301) / 3 = 1122 / 3 ≈ 374
This solution is correct!
Solution 5:
929, 107, 86
Verification:
(929 + 107 + 86) / 3 = 1122 / 3 ≈ 374
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 1122 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.