What three numbers have an average of 978?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 978. This means if we add these three numbers together and divide by 3, we should get 978.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 978 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 978 * 3 = x + y + z
- So, the sum of our three numbers should be: 2934
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2934.
Solution 1:
978, 978, 978
Verification:
(978 + 978 + 978) / 3 = 2934 / 3 ≈ 978
This solution is correct!
Solution 2:
978, 978, 978
Verification:
(978 + 978 + 978) / 3 = 2934 / 3 ≈ 978
This solution is correct!
Solution 3:
330, 2152, 452
Verification:
(330 + 2152 + 452) / 3 = 2934 / 3 ≈ 978
This solution is correct!
Solution 4:
2229, 222, 483
Verification:
(2229 + 222 + 483) / 3 = 2934 / 3 ≈ 978
This solution is correct!
Solution 5:
470, 1452, 1012
Verification:
(470 + 1452 + 1012) / 3 = 2934 / 3 ≈ 978
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 2934 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.