What three numbers have an average of 61?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 61. This means if we add these three numbers together and divide by 3, we should get 61.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 61 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 61 * 3 = x + y + z
- So, the sum of our three numbers should be: 183
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 183.
Solution 1:
61, 61, 61
Verification:
(61 + 61 + 61) / 3 = 183 / 3 ≈ 61
This solution is correct!
Solution 2:
61, 61, 61
Verification:
(61 + 61 + 61) / 3 = 183 / 3 ≈ 61
This solution is correct!
Solution 3:
148, 16, 19
Verification:
(148 + 16 + 19) / 3 = 183 / 3 ≈ 61
This solution is correct!
Solution 4:
76, 48, 59
Verification:
(76 + 48 + 59) / 3 = 183 / 3 ≈ 61
This solution is correct!
Solution 5:
140, 38, 5
Verification:
(140 + 38 + 5) / 3 = 183 / 3 ≈ 61
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 183 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.