What three numbers have an average of 56?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 56. This means if we add these three numbers together and divide by 3, we should get 56.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 56 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 56 * 3 = x + y + z
- So, the sum of our three numbers should be: 168
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 168.
Solution 1:
56, 56, 56
Verification:
(56 + 56 + 56) / 3 = 168 / 3 ≈ 56
This solution is correct!
Solution 2:
56, 56, 56
Verification:
(56 + 56 + 56) / 3 = 168 / 3 ≈ 56
This solution is correct!
Solution 3:
23, 140, 5
Verification:
(23 + 140 + 5) / 3 = 168 / 3 ≈ 56
This solution is correct!
Solution 4:
112, 16, 40
Verification:
(112 + 16 + 40) / 3 = 168 / 3 ≈ 56
This solution is correct!
Solution 5:
91, 45, 32
Verification:
(91 + 45 + 32) / 3 = 168 / 3 ≈ 56
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 168 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.