What three numbers have an average of 429?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 429. This means if we add these three numbers together and divide by 3, we should get 429.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 429 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 429 * 3 = x + y + z
- So, the sum of our three numbers should be: 1287
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1287.
Solution 1:
429, 429, 429
Verification:
(429 + 429 + 429) / 3 = 1287 / 3 ≈ 429
This solution is correct!
Solution 2:
429, 429, 429
Verification:
(429 + 429 + 429) / 3 = 1287 / 3 ≈ 429
This solution is correct!
Solution 3:
1277, 9, 1
Verification:
(1277 + 9 + 1) / 3 = 1287 / 3 ≈ 429
This solution is correct!
Solution 4:
1060, 94, 133
Verification:
(1060 + 94 + 133) / 3 = 1287 / 3 ≈ 429
This solution is correct!
Solution 5:
729, 314, 244
Verification:
(729 + 314 + 244) / 3 = 1287 / 3 ≈ 429
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 1287 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.