What three numbers have an average of 282?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 282. This means if we add these three numbers together and divide by 3, we should get 282.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 282 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 282 * 3 = x + y + z
- So, the sum of our three numbers should be: 846
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 846.
Solution 1:
282, 282, 282
Verification:
(282 + 282 + 282) / 3 = 846 / 3 ≈ 282
This solution is correct!
Solution 2:
282, 282, 282
Verification:
(282 + 282 + 282) / 3 = 846 / 3 ≈ 282
This solution is correct!
Solution 3:
570, 80, 196
Verification:
(570 + 80 + 196) / 3 = 846 / 3 ≈ 282
This solution is correct!
Solution 4:
493, 142, 211
Verification:
(493 + 142 + 211) / 3 = 846 / 3 ≈ 282
This solution is correct!
Solution 5:
416, 104, 326
Verification:
(416 + 104 + 326) / 3 = 846 / 3 ≈ 282
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 846 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.