What three numbers have an average of 170?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 170. This means if we add these three numbers together and divide by 3, we should get 170.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 170 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 170 * 3 = x + y + z
- So, the sum of our three numbers should be: 510
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 510.
Solution 1:
170, 170, 170
Verification:
(170 + 170 + 170) / 3 = 510 / 3 ≈ 170
This solution is correct!
Solution 2:
170, 170, 170
Verification:
(170 + 170 + 170) / 3 = 510 / 3 ≈ 170
This solution is correct!
Solution 3:
205, 99, 206
Verification:
(205 + 99 + 206) / 3 = 510 / 3 ≈ 170
This solution is correct!
Solution 4:
454, 40, 16
Verification:
(454 + 40 + 16) / 3 = 510 / 3 ≈ 170
This solution is correct!
Solution 5:
172, 337, 1
Verification:
(172 + 337 + 1) / 3 = 510 / 3 ≈ 170
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 510 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.