What three numbers have an average of 80?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 80. This means if we add these three numbers together and divide by 3, we should get 80.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 80 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 80 * 3 = x + y + z
- So, the sum of our three numbers should be: 240
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 240.
Solution 1:
80, 80, 80
Verification:
(80 + 80 + 80) / 3 = 240 / 3 ≈ 80
This solution is correct!
Solution 2:
80, 80, 80
Verification:
(80 + 80 + 80) / 3 = 240 / 3 ≈ 80
This solution is correct!
Solution 3:
1, 174, 65
Verification:
(1 + 174 + 65) / 3 = 240 / 3 ≈ 80
This solution is correct!
Solution 4:
78, 99, 63
Verification:
(78 + 99 + 63) / 3 = 240 / 3 ≈ 80
This solution is correct!
Solution 5:
185, 50, 5
Verification:
(185 + 50 + 5) / 3 = 240 / 3 ≈ 80
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 240 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.