What three numbers have an average of 124?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 124. This means if we add these three numbers together and divide by 3, we should get 124.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 124 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 124 * 3 = x + y + z
- So, the sum of our three numbers should be: 372
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 372.
Solution 1:
124, 124, 124
Verification:
(124 + 124 + 124) / 3 = 372 / 3 ≈ 124
This solution is correct!
Solution 2:
124, 124, 124
Verification:
(124 + 124 + 124) / 3 = 372 / 3 ≈ 124
This solution is correct!
Solution 3:
116, 159, 97
Verification:
(116 + 159 + 97) / 3 = 372 / 3 ≈ 124
This solution is correct!
Solution 4:
51, 218, 103
Verification:
(51 + 218 + 103) / 3 = 372 / 3 ≈ 124
This solution is correct!
Solution 5:
153, 86, 133
Verification:
(153 + 86 + 133) / 3 = 372 / 3 ≈ 124
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 372 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.