What three numbers have an average of 661?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 661. This means if we add these three numbers together and divide by 3, we should get 661.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 661 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 661 * 3 = x + y + z
- So, the sum of our three numbers should be: 1983
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1983.
Solution 1:
661, 661, 661
Verification:
(661 + 661 + 661) / 3 = 1983 / 3 ≈ 661
This solution is correct!
Solution 2:
661, 661, 661
Verification:
(661 + 661 + 661) / 3 = 1983 / 3 ≈ 661
This solution is correct!
Solution 3:
574, 738, 671
Verification:
(574 + 738 + 671) / 3 = 1983 / 3 ≈ 661
This solution is correct!
Solution 4:
88, 354, 1541
Verification:
(88 + 354 + 1541) / 3 = 1983 / 3 ≈ 661
This solution is correct!
Solution 5:
1864, 56, 63
Verification:
(1864 + 56 + 63) / 3 = 1983 / 3 ≈ 661
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 1983 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.