What three numbers have an average of 71?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 71. This means if we add these three numbers together and divide by 3, we should get 71.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 71 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 71 * 3 = x + y + z
- So, the sum of our three numbers should be: 213
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 213.
Solution 1:
71, 71, 71
Verification:
(71 + 71 + 71) / 3 = 213 / 3 ≈ 71
This solution is correct!
Solution 2:
71, 71, 71
Verification:
(71 + 71 + 71) / 3 = 213 / 3 ≈ 71
This solution is correct!
Solution 3:
87, 19, 107
Verification:
(87 + 19 + 107) / 3 = 213 / 3 ≈ 71
This solution is correct!
Solution 4:
35, 61, 117
Verification:
(35 + 61 + 117) / 3 = 213 / 3 ≈ 71
This solution is correct!
Solution 5:
59, 81, 73
Verification:
(59 + 81 + 73) / 3 = 213 / 3 ≈ 71
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 213 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.