What three numbers have an average of 74?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 74. This means if we add these three numbers together and divide by 3, we should get 74.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 74 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 74 * 3 = x + y + z
- So, the sum of our three numbers should be: 222
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 222.
Solution 1:
74, 74, 74
Verification:
(74 + 74 + 74) / 3 = 222 / 3 ≈ 74
This solution is correct!
Solution 2:
74, 74, 74
Verification:
(74 + 74 + 74) / 3 = 222 / 3 ≈ 74
This solution is correct!
Solution 3:
214, 5, 3
Verification:
(214 + 5 + 3) / 3 = 222 / 3 ≈ 74
This solution is correct!
Solution 4:
155, 41, 26
Verification:
(155 + 41 + 26) / 3 = 222 / 3 ≈ 74
This solution is correct!
Solution 5:
20, 62, 140
Verification:
(20 + 62 + 140) / 3 = 222 / 3 ≈ 74
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 222 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.