What three numbers have an average of 278?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 278. This means if we add these three numbers together and divide by 3, we should get 278.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 278 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 278 * 3 = x + y + z
- So, the sum of our three numbers should be: 834
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 834.
Solution 1:
278, 278, 278
Verification:
(278 + 278 + 278) / 3 = 834 / 3 ≈ 278
This solution is correct!
Solution 2:
278, 278, 278
Verification:
(278 + 278 + 278) / 3 = 834 / 3 ≈ 278
This solution is correct!
Solution 3:
406, 377, 51
Verification:
(406 + 377 + 51) / 3 = 834 / 3 ≈ 278
This solution is correct!
Solution 4:
237, 24, 573
Verification:
(237 + 24 + 573) / 3 = 834 / 3 ≈ 278
This solution is correct!
Solution 5:
55, 266, 513
Verification:
(55 + 266 + 513) / 3 = 834 / 3 ≈ 278
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 834 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.