What three numbers have an average of 520?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 520. This means if we add these three numbers together and divide by 3, we should get 520.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 520 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 520 * 3 = x + y + z
- So, the sum of our three numbers should be: 1560
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1560.
Solution 1:
520, 520, 520
Verification:
(520 + 520 + 520) / 3 = 1560 / 3 ≈ 520
This solution is correct!
Solution 2:
520, 520, 520
Verification:
(520 + 520 + 520) / 3 = 1560 / 3 ≈ 520
This solution is correct!
Solution 3:
329, 950, 281
Verification:
(329 + 950 + 281) / 3 = 1560 / 3 ≈ 520
This solution is correct!
Solution 4:
45, 1002, 513
Verification:
(45 + 1002 + 513) / 3 = 1560 / 3 ≈ 520
This solution is correct!
Solution 5:
733, 480, 347
Verification:
(733 + 480 + 347) / 3 = 1560 / 3 ≈ 520
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 1560 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.