What three numbers have an average of 90?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 90. This means if we add these three numbers together and divide by 3, we should get 90.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 90 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 90 * 3 = x + y + z
- So, the sum of our three numbers should be: 270
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 270.
Solution 1:
90, 90, 90
Verification:
(90 + 90 + 90) / 3 = 270 / 3 ≈ 90
This solution is correct!
Solution 2:
90, 90, 90
Verification:
(90 + 90 + 90) / 3 = 270 / 3 ≈ 90
This solution is correct!
Solution 3:
138, 80, 52
Verification:
(138 + 80 + 52) / 3 = 270 / 3 ≈ 90
This solution is correct!
Solution 4:
72, 76, 122
Verification:
(72 + 76 + 122) / 3 = 270 / 3 ≈ 90
This solution is correct!
Solution 5:
192, 29, 49
Verification:
(192 + 29 + 49) / 3 = 270 / 3 ≈ 90
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 270 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.