What three numbers have an average of 732?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 732. This means if we add these three numbers together and divide by 3, we should get 732.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 732 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 732 * 3 = x + y + z
- So, the sum of our three numbers should be: 2196
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2196.
Solution 1:
732, 732, 732
Verification:
(732 + 732 + 732) / 3 = 2196 / 3 ≈ 732
This solution is correct!
Solution 2:
732, 732, 732
Verification:
(732 + 732 + 732) / 3 = 2196 / 3 ≈ 732
This solution is correct!
Solution 3:
1271, 459, 466
Verification:
(1271 + 459 + 466) / 3 = 2196 / 3 ≈ 732
This solution is correct!
Solution 4:
1648, 79, 469
Verification:
(1648 + 79 + 469) / 3 = 2196 / 3 ≈ 732
This solution is correct!
Solution 5:
419, 1081, 696
Verification:
(419 + 1081 + 696) / 3 = 2196 / 3 ≈ 732
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 2196 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.