What three numbers have an average of 870?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 870. This means if we add these three numbers together and divide by 3, we should get 870.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 870 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 870 * 3 = x + y + z
- So, the sum of our three numbers should be: 2610
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2610.
Solution 1:
870, 870, 870
Verification:
(870 + 870 + 870) / 3 = 2610 / 3 ≈ 870
This solution is correct!
Solution 2:
870, 870, 870
Verification:
(870 + 870 + 870) / 3 = 2610 / 3 ≈ 870
This solution is correct!
Solution 3:
74, 567, 1969
Verification:
(74 + 567 + 1969) / 3 = 2610 / 3 ≈ 870
This solution is correct!
Solution 4:
1643, 143, 824
Verification:
(1643 + 143 + 824) / 3 = 2610 / 3 ≈ 870
This solution is correct!
Solution 5:
1727, 463, 420
Verification:
(1727 + 463 + 420) / 3 = 2610 / 3 ≈ 870
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 2610 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.