What three numbers have an average of 670?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 670. This means if we add these three numbers together and divide by 3, we should get 670.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 670 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 670 * 3 = x + y + z
- So, the sum of our three numbers should be: 2010
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2010.
Solution 1:
670, 670, 670
Verification:
(670 + 670 + 670) / 3 = 2010 / 3 ≈ 670
This solution is correct!
Solution 2:
670, 670, 670
Verification:
(670 + 670 + 670) / 3 = 2010 / 3 ≈ 670
This solution is correct!
Solution 3:
157, 1752, 101
Verification:
(157 + 1752 + 101) / 3 = 2010 / 3 ≈ 670
This solution is correct!
Solution 4:
1838, 89, 83
Verification:
(1838 + 89 + 83) / 3 = 2010 / 3 ≈ 670
This solution is correct!
Solution 5:
1023, 113, 874
Verification:
(1023 + 113 + 874) / 3 = 2010 / 3 ≈ 670
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 2010 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.