What three numbers have an average of 716?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 716. This means if we add these three numbers together and divide by 3, we should get 716.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 716 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 716 * 3 = x + y + z
- So, the sum of our three numbers should be: 2148
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2148.
Solution 1:
716, 716, 716
Verification:
(716 + 716 + 716) / 3 = 2148 / 3 ≈ 716
This solution is correct!
Solution 2:
716, 716, 716
Verification:
(716 + 716 + 716) / 3 = 2148 / 3 ≈ 716
This solution is correct!
Solution 3:
1200, 95, 853
Verification:
(1200 + 95 + 853) / 3 = 2148 / 3 ≈ 716
This solution is correct!
Solution 4:
1620, 106, 422
Verification:
(1620 + 106 + 422) / 3 = 2148 / 3 ≈ 716
This solution is correct!
Solution 5:
30, 241, 1877
Verification:
(30 + 241 + 1877) / 3 = 2148 / 3 ≈ 716
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 2148 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.