What three numbers have an average of 160?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 160. This means if we add these three numbers together and divide by 3, we should get 160.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 160 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 160 * 3 = x + y + z
- So, the sum of our three numbers should be: 480
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 480.
Solution 1:
160, 160, 160
Verification:
(160 + 160 + 160) / 3 = 480 / 3 ≈ 160
This solution is correct!
Solution 2:
160, 160, 160
Verification:
(160 + 160 + 160) / 3 = 480 / 3 ≈ 160
This solution is correct!
Solution 3:
183, 208, 89
Verification:
(183 + 208 + 89) / 3 = 480 / 3 ≈ 160
This solution is correct!
Solution 4:
119, 214, 147
Verification:
(119 + 214 + 147) / 3 = 480 / 3 ≈ 160
This solution is correct!
Solution 5:
90, 318, 72
Verification:
(90 + 318 + 72) / 3 = 480 / 3 ≈ 160
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 480 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.