What three numbers have an average of 528?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 528. This means if we add these three numbers together and divide by 3, we should get 528.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 528 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 528 * 3 = x + y + z
- So, the sum of our three numbers should be: 1584
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1584.
Solution 1:
528, 528, 528
Verification:
(528 + 528 + 528) / 3 = 1584 / 3 ≈ 528
This solution is correct!
Solution 2:
528, 528, 528
Verification:
(528 + 528 + 528) / 3 = 1584 / 3 ≈ 528
This solution is correct!
Solution 3:
78, 208, 1298
Verification:
(78 + 208 + 1298) / 3 = 1584 / 3 ≈ 528
This solution is correct!
Solution 4:
3, 349, 1232
Verification:
(3 + 349 + 1232) / 3 = 1584 / 3 ≈ 528
This solution is correct!
Solution 5:
518, 1040, 26
Verification:
(518 + 1040 + 26) / 3 = 1584 / 3 ≈ 528
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 1584 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.