What three numbers have an average of 760?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 760. This means if we add these three numbers together and divide by 3, we should get 760.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 760 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 760 * 3 = x + y + z
- So, the sum of our three numbers should be: 2280
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2280.
Solution 1:
760, 760, 760
Verification:
(760 + 760 + 760) / 3 = 2280 / 3 ≈ 760
This solution is correct!
Solution 2:
760, 760, 760
Verification:
(760 + 760 + 760) / 3 = 2280 / 3 ≈ 760
This solution is correct!
Solution 3:
1338, 654, 288
Verification:
(1338 + 654 + 288) / 3 = 2280 / 3 ≈ 760
This solution is correct!
Solution 4:
1697, 324, 259
Verification:
(1697 + 324 + 259) / 3 = 2280 / 3 ≈ 760
This solution is correct!
Solution 5:
714, 34, 1532
Verification:
(714 + 34 + 1532) / 3 = 2280 / 3 ≈ 760
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 2280 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.