What three numbers have an average of 77?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 77. This means if we add these three numbers together and divide by 3, we should get 77.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 77 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 77 * 3 = x + y + z
- So, the sum of our three numbers should be: 231
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 231.
Solution 1:
77, 77, 77
Verification:
(77 + 77 + 77) / 3 = 231 / 3 ≈ 77
This solution is correct!
Solution 2:
77, 77, 77
Verification:
(77 + 77 + 77) / 3 = 231 / 3 ≈ 77
This solution is correct!
Solution 3:
115, 48, 68
Verification:
(115 + 48 + 68) / 3 = 231 / 3 ≈ 77
This solution is correct!
Solution 4:
171, 57, 3
Verification:
(171 + 57 + 3) / 3 = 231 / 3 ≈ 77
This solution is correct!
Solution 5:
123, 20, 88
Verification:
(123 + 20 + 88) / 3 = 231 / 3 ≈ 77
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 231 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.