What three numbers have an average of 76?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 76. This means if we add these three numbers together and divide by 3, we should get 76.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 76 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 76 * 3 = x + y + z
- So, the sum of our three numbers should be: 228
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 228.
Solution 1:
76, 76, 76
Verification:
(76 + 76 + 76) / 3 = 228 / 3 ≈ 76
This solution is correct!
Solution 2:
76, 76, 76
Verification:
(76 + 76 + 76) / 3 = 228 / 3 ≈ 76
This solution is correct!
Solution 3:
65, 117, 46
Verification:
(65 + 117 + 46) / 3 = 228 / 3 ≈ 76
This solution is correct!
Solution 4:
5, 73, 150
Verification:
(5 + 73 + 150) / 3 = 228 / 3 ≈ 76
This solution is correct!
Solution 5:
116, 110, 2
Verification:
(116 + 110 + 2) / 3 = 228 / 3 ≈ 76
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 228 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.