What three numbers have an average of 213?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 213. This means if we add these three numbers together and divide by 3, we should get 213.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 213 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 213 * 3 = x + y + z
- So, the sum of our three numbers should be: 639
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 639.
Solution 1:
213, 213, 213
Verification:
(213 + 213 + 213) / 3 = 639 / 3 ≈ 213
This solution is correct!
Solution 2:
213, 213, 213
Verification:
(213 + 213 + 213) / 3 = 639 / 3 ≈ 213
This solution is correct!
Solution 3:
598, 33, 8
Verification:
(598 + 33 + 8) / 3 = 639 / 3 ≈ 213
This solution is correct!
Solution 4:
257, 254, 128
Verification:
(257 + 254 + 128) / 3 = 639 / 3 ≈ 213
This solution is correct!
Solution 5:
421, 43, 175
Verification:
(421 + 43 + 175) / 3 = 639 / 3 ≈ 213
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 639 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.