What three numbers have an average of 526?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 526. This means if we add these three numbers together and divide by 3, we should get 526.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 526 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 526 * 3 = x + y + z
- So, the sum of our three numbers should be: 1578
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1578.
Solution 1:
526, 526, 526
Verification:
(526 + 526 + 526) / 3 = 1578 / 3 ≈ 526
This solution is correct!
Solution 2:
526, 526, 526
Verification:
(526 + 526 + 526) / 3 = 1578 / 3 ≈ 526
This solution is correct!
Solution 3:
1014, 394, 170
Verification:
(1014 + 394 + 170) / 3 = 1578 / 3 ≈ 526
This solution is correct!
Solution 4:
765, 31, 782
Verification:
(765 + 31 + 782) / 3 = 1578 / 3 ≈ 526
This solution is correct!
Solution 5:
1352, 143, 83
Verification:
(1352 + 143 + 83) / 3 = 1578 / 3 ≈ 526
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 1578 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.