What three numbers have an average of 147?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 147. This means if we add these three numbers together and divide by 3, we should get 147.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 147 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 147 * 3 = x + y + z
- So, the sum of our three numbers should be: 441
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 441.
Solution 1:
147, 147, 147
Verification:
(147 + 147 + 147) / 3 = 441 / 3 ≈ 147
This solution is correct!
Solution 2:
147, 147, 147
Verification:
(147 + 147 + 147) / 3 = 441 / 3 ≈ 147
This solution is correct!
Solution 3:
87, 25, 329
Verification:
(87 + 25 + 329) / 3 = 441 / 3 ≈ 147
This solution is correct!
Solution 4:
187, 252, 2
Verification:
(187 + 252 + 2) / 3 = 441 / 3 ≈ 147
This solution is correct!
Solution 5:
278, 73, 90
Verification:
(278 + 73 + 90) / 3 = 441 / 3 ≈ 147
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 441 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.