What three numbers have an average of 78?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 78. This means if we add these three numbers together and divide by 3, we should get 78.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 78 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 78 * 3 = x + y + z
- So, the sum of our three numbers should be: 234
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 234.
Solution 1:
78, 78, 78
Verification:
(78 + 78 + 78) / 3 = 234 / 3 ≈ 78
This solution is correct!
Solution 2:
78, 78, 78
Verification:
(78 + 78 + 78) / 3 = 234 / 3 ≈ 78
This solution is correct!
Solution 3:
206, 18, 10
Verification:
(206 + 18 + 10) / 3 = 234 / 3 ≈ 78
This solution is correct!
Solution 4:
174, 19, 41
Verification:
(174 + 19 + 41) / 3 = 234 / 3 ≈ 78
This solution is correct!
Solution 5:
145, 12, 77
Verification:
(145 + 12 + 77) / 3 = 234 / 3 ≈ 78
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 234 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.