What three numbers have an average of 210?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 210. This means if we add these three numbers together and divide by 3, we should get 210.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 210 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 210 * 3 = x + y + z
- So, the sum of our three numbers should be: 630
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 630.
Solution 1:
210, 210, 210
Verification:
(210 + 210 + 210) / 3 = 630 / 3 ≈ 210
This solution is correct!
Solution 2:
210, 210, 210
Verification:
(210 + 210 + 210) / 3 = 630 / 3 ≈ 210
This solution is correct!
Solution 3:
332, 41, 257
Verification:
(332 + 41 + 257) / 3 = 630 / 3 ≈ 210
This solution is correct!
Solution 4:
147, 27, 456
Verification:
(147 + 27 + 456) / 3 = 630 / 3 ≈ 210
This solution is correct!
Solution 5:
257, 301, 72
Verification:
(257 + 301 + 72) / 3 = 630 / 3 ≈ 210
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 630 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.