What three numbers have an average of 758?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 758. This means if we add these three numbers together and divide by 3, we should get 758.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 758 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 758 * 3 = x + y + z
- So, the sum of our three numbers should be: 2274
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2274.
Solution 1:
758, 758, 758
Verification:
(758 + 758 + 758) / 3 = 2274 / 3 ≈ 758
This solution is correct!
Solution 2:
758, 758, 758
Verification:
(758 + 758 + 758) / 3 = 2274 / 3 ≈ 758
This solution is correct!
Solution 3:
336, 502, 1436
Verification:
(336 + 502 + 1436) / 3 = 2274 / 3 ≈ 758
This solution is correct!
Solution 4:
773, 1058, 443
Verification:
(773 + 1058 + 443) / 3 = 2274 / 3 ≈ 758
This solution is correct!
Solution 5:
1149, 1008, 117
Verification:
(1149 + 1008 + 117) / 3 = 2274 / 3 ≈ 758
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 2274 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.