What three numbers have an average of 89?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 89. This means if we add these three numbers together and divide by 3, we should get 89.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 89 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 89 * 3 = x + y + z
- So, the sum of our three numbers should be: 267
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 267.
Solution 1:
89, 89, 89
Verification:
(89 + 89 + 89) / 3 = 267 / 3 ≈ 89
This solution is correct!
Solution 2:
89, 89, 89
Verification:
(89 + 89 + 89) / 3 = 267 / 3 ≈ 89
This solution is correct!
Solution 3:
21, 211, 35
Verification:
(21 + 211 + 35) / 3 = 267 / 3 ≈ 89
This solution is correct!
Solution 4:
43, 130, 94
Verification:
(43 + 130 + 94) / 3 = 267 / 3 ≈ 89
This solution is correct!
Solution 5:
116, 68, 83
Verification:
(116 + 68 + 83) / 3 = 267 / 3 ≈ 89
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 267 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.