What three numbers have an average of 464?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 464. This means if we add these three numbers together and divide by 3, we should get 464.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 464 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 464 * 3 = x + y + z
- So, the sum of our three numbers should be: 1392
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1392.
Solution 1:
464, 464, 464
Verification:
(464 + 464 + 464) / 3 = 1392 / 3 ≈ 464
This solution is correct!
Solution 2:
464, 464, 464
Verification:
(464 + 464 + 464) / 3 = 1392 / 3 ≈ 464
This solution is correct!
Solution 3:
46, 261, 1085
Verification:
(46 + 261 + 1085) / 3 = 1392 / 3 ≈ 464
This solution is correct!
Solution 4:
1250, 123, 19
Verification:
(1250 + 123 + 19) / 3 = 1392 / 3 ≈ 464
This solution is correct!
Solution 5:
912, 112, 368
Verification:
(912 + 112 + 368) / 3 = 1392 / 3 ≈ 464
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 1392 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.