What three numbers have an average of 118?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 118. This means if we add these three numbers together and divide by 3, we should get 118.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 118 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 118 * 3 = x + y + z
- So, the sum of our three numbers should be: 354
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 354.
Solution 1:
118, 118, 118
Verification:
(118 + 118 + 118) / 3 = 354 / 3 ≈ 118
This solution is correct!
Solution 2:
118, 118, 118
Verification:
(118 + 118 + 118) / 3 = 354 / 3 ≈ 118
This solution is correct!
Solution 3:
119, 99, 136
Verification:
(119 + 99 + 136) / 3 = 354 / 3 ≈ 118
This solution is correct!
Solution 4:
347, 1, 6
Verification:
(347 + 1 + 6) / 3 = 354 / 3 ≈ 118
This solution is correct!
Solution 5:
182, 31, 141
Verification:
(182 + 31 + 141) / 3 = 354 / 3 ≈ 118
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 354 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.