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:
120, 4, 53
Verification:
(120 + 4 + 53) / 3 = 177 / 3 ≈ 59
This solution is correct!
Solution 4:
22, 81, 74
Verification:
(22 + 81 + 74) / 3 = 177 / 3 ≈ 59
This solution is correct!
Solution 5:
113, 13, 51
Verification:
(113 + 13 + 51) / 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.