What three numbers have an average of 91?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 91. This means if we add these three numbers together and divide by 3, we should get 91.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 91 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 91 * 3 = x + y + z
- So, the sum of our three numbers should be: 273
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 273.
Solution 1:
91, 91, 91
Verification:
(91 + 91 + 91) / 3 = 273 / 3 ≈ 91
This solution is correct!
Solution 2:
91, 91, 91
Verification:
(91 + 91 + 91) / 3 = 273 / 3 ≈ 91
This solution is correct!
Solution 3:
233, 34, 6
Verification:
(233 + 34 + 6) / 3 = 273 / 3 ≈ 91
This solution is correct!
Solution 4:
120, 5, 148
Verification:
(120 + 5 + 148) / 3 = 273 / 3 ≈ 91
This solution is correct!
Solution 5:
52, 51, 170
Verification:
(52 + 51 + 170) / 3 = 273 / 3 ≈ 91
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 273 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.