What three numbers have an average of 172?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 172. This means if we add these three numbers together and divide by 3, we should get 172.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 172 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 172 * 3 = x + y + z
- So, the sum of our three numbers should be: 516
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 516.
Solution 1:
172, 172, 172
Verification:
(172 + 172 + 172) / 3 = 516 / 3 ≈ 172
This solution is correct!
Solution 2:
172, 172, 172
Verification:
(172 + 172 + 172) / 3 = 516 / 3 ≈ 172
This solution is correct!
Solution 3:
175, 314, 27
Verification:
(175 + 314 + 27) / 3 = 516 / 3 ≈ 172
This solution is correct!
Solution 4:
350, 24, 142
Verification:
(350 + 24 + 142) / 3 = 516 / 3 ≈ 172
This solution is correct!
Solution 5:
368, 16, 132
Verification:
(368 + 16 + 132) / 3 = 516 / 3 ≈ 172
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 516 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.