What three numbers have an average of 689?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 689. This means if we add these three numbers together and divide by 3, we should get 689.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 689 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 689 * 3 = x + y + z
- So, the sum of our three numbers should be: 2067
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2067.
Solution 1:
689, 689, 689
Verification:
(689 + 689 + 689) / 3 = 2067 / 3 ≈ 689
This solution is correct!
Solution 2:
689, 689, 689
Verification:
(689 + 689 + 689) / 3 = 2067 / 3 ≈ 689
This solution is correct!
Solution 3:
1742, 177, 148
Verification:
(1742 + 177 + 148) / 3 = 2067 / 3 ≈ 689
This solution is correct!
Solution 4:
1199, 516, 352
Verification:
(1199 + 516 + 352) / 3 = 2067 / 3 ≈ 689
This solution is correct!
Solution 5:
1743, 26, 298
Verification:
(1743 + 26 + 298) / 3 = 2067 / 3 ≈ 689
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 2067 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.