What three numbers have an average of 402?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 402. This means if we add these three numbers together and divide by 3, we should get 402.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 402 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 402 * 3 = x + y + z
- So, the sum of our three numbers should be: 1206
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1206.
Solution 1:
402, 402, 402
Verification:
(402 + 402 + 402) / 3 = 1206 / 3 ≈ 402
This solution is correct!
Solution 2:
402, 402, 402
Verification:
(402 + 402 + 402) / 3 = 1206 / 3 ≈ 402
This solution is correct!
Solution 3:
438, 499, 269
Verification:
(438 + 499 + 269) / 3 = 1206 / 3 ≈ 402
This solution is correct!
Solution 4:
1174, 15, 17
Verification:
(1174 + 15 + 17) / 3 = 1206 / 3 ≈ 402
This solution is correct!
Solution 5:
366, 340, 500
Verification:
(366 + 340 + 500) / 3 = 1206 / 3 ≈ 402
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 1206 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.