What three numbers have an average of 980?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 980. This means if we add these three numbers together and divide by 3, we should get 980.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 980 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 980 * 3 = x + y + z
- So, the sum of our three numbers should be: 2940
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2940.
Solution 1:
980, 980, 980
Verification:
(980 + 980 + 980) / 3 = 2940 / 3 ≈ 980
This solution is correct!
Solution 2:
980, 980, 980
Verification:
(980 + 980 + 980) / 3 = 2940 / 3 ≈ 980
This solution is correct!
Solution 3:
1749, 182, 1009
Verification:
(1749 + 182 + 1009) / 3 = 2940 / 3 ≈ 980
This solution is correct!
Solution 4:
67, 945, 1928
Verification:
(67 + 945 + 1928) / 3 = 2940 / 3 ≈ 980
This solution is correct!
Solution 5:
2837, 55, 48
Verification:
(2837 + 55 + 48) / 3 = 2940 / 3 ≈ 980
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 2940 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.