What three numbers have an average of 67?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 67. This means if we add these three numbers together and divide by 3, we should get 67.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 67 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 67 * 3 = x + y + z
- So, the sum of our three numbers should be: 201
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 201.
Solution 1:
67, 67, 67
Verification:
(67 + 67 + 67) / 3 = 201 / 3 ≈ 67
This solution is correct!
Solution 2:
67, 67, 67
Verification:
(67 + 67 + 67) / 3 = 201 / 3 ≈ 67
This solution is correct!
Solution 3:
100, 82, 19
Verification:
(100 + 82 + 19) / 3 = 201 / 3 ≈ 67
This solution is correct!
Solution 4:
178, 4, 19
Verification:
(178 + 4 + 19) / 3 = 201 / 3 ≈ 67
This solution is correct!
Solution 5:
175, 3, 23
Verification:
(175 + 3 + 23) / 3 = 201 / 3 ≈ 67
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 201 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.