What three numbers have an average of 93?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 93. This means if we add these three numbers together and divide by 3, we should get 93.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 93 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 93 * 3 = x + y + z
- So, the sum of our three numbers should be: 279
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 279.
Solution 1:
93, 93, 93
Verification:
(93 + 93 + 93) / 3 = 279 / 3 ≈ 93
This solution is correct!
Solution 2:
93, 93, 93
Verification:
(93 + 93 + 93) / 3 = 279 / 3 ≈ 93
This solution is correct!
Solution 3:
99, 6, 174
Verification:
(99 + 6 + 174) / 3 = 279 / 3 ≈ 93
This solution is correct!
Solution 4:
41, 115, 123
Verification:
(41 + 115 + 123) / 3 = 279 / 3 ≈ 93
This solution is correct!
Solution 5:
181, 35, 63
Verification:
(181 + 35 + 63) / 3 = 279 / 3 ≈ 93
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 279 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.