What three numbers have an average of 59?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 59. This means if we add these three numbers together and divide by 3, we should get 59.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 59 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 59 * 3 = x + y + z
- So, the sum of our three numbers should be: 177
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 177.
Solution 1:
59, 59, 59
Verification:
(59 + 59 + 59) / 3 = 177 / 3 ≈ 59
This solution is correct!
Solution 2:
59, 59, 59
Verification:
(59 + 59 + 59) / 3 = 177 / 3 ≈ 59
This solution is correct!
Solution 3:
37, 79, 61
Verification:
(37 + 79 + 61) / 3 = 177 / 3 ≈ 59
This solution is correct!
Solution 4:
19, 151, 7
Verification:
(19 + 151 + 7) / 3 = 177 / 3 ≈ 59
This solution is correct!
Solution 5:
160, 8, 9
Verification:
(160 + 8 + 9) / 3 = 177 / 3 ≈ 59
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 177 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.