What three numbers have an average of 262?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 262. This means if we add these three numbers together and divide by 3, we should get 262.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 262 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 262 * 3 = x + y + z
- So, the sum of our three numbers should be: 786
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 786.
Solution 1:
262, 262, 262
Verification:
(262 + 262 + 262) / 3 = 786 / 3 ≈ 262
This solution is correct!
Solution 2:
262, 262, 262
Verification:
(262 + 262 + 262) / 3 = 786 / 3 ≈ 262
This solution is correct!
Solution 3:
23, 254, 509
Verification:
(23 + 254 + 509) / 3 = 786 / 3 ≈ 262
This solution is correct!
Solution 4:
496, 49, 241
Verification:
(496 + 49 + 241) / 3 = 786 / 3 ≈ 262
This solution is correct!
Solution 5:
147, 210, 429
Verification:
(147 + 210 + 429) / 3 = 786 / 3 ≈ 262
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 786 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.