What three numbers have an average of 652?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 652. This means if we add these three numbers together and divide by 3, we should get 652.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 652 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 652 * 3 = x + y + z
- So, the sum of our three numbers should be: 1956
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1956.
Solution 1:
652, 652, 652
Verification:
(652 + 652 + 652) / 3 = 1956 / 3 ≈ 652
This solution is correct!
Solution 2:
652, 652, 652
Verification:
(652 + 652 + 652) / 3 = 1956 / 3 ≈ 652
This solution is correct!
Solution 3:
1648, 273, 35
Verification:
(1648 + 273 + 35) / 3 = 1956 / 3 ≈ 652
This solution is correct!
Solution 4:
1520, 284, 152
Verification:
(1520 + 284 + 152) / 3 = 1956 / 3 ≈ 652
This solution is correct!
Solution 5:
860, 141, 955
Verification:
(860 + 141 + 955) / 3 = 1956 / 3 ≈ 652
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 1956 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.