What three numbers have an average of 840?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 840. This means if we add these three numbers together and divide by 3, we should get 840.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 840 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 840 * 3 = x + y + z
- So, the sum of our three numbers should be: 2520
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2520.
Solution 1:
840, 840, 840
Verification:
(840 + 840 + 840) / 3 = 2520 / 3 ≈ 840
This solution is correct!
Solution 2:
840, 840, 840
Verification:
(840 + 840 + 840) / 3 = 2520 / 3 ≈ 840
This solution is correct!
Solution 3:
2403, 6, 111
Verification:
(2403 + 6 + 111) / 3 = 2520 / 3 ≈ 840
This solution is correct!
Solution 4:
424, 1300, 796
Verification:
(424 + 1300 + 796) / 3 = 2520 / 3 ≈ 840
This solution is correct!
Solution 5:
2095, 133, 292
Verification:
(2095 + 133 + 292) / 3 = 2520 / 3 ≈ 840
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 2520 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.