What three numbers have an average of 35?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 35. This means if we add these three numbers together and divide by 3, we should get 35.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 35 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 35 * 3 = x + y + z
- So, the sum of our three numbers should be: 105
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 105.
Solution 1:
35, 35, 35
Verification:
(35 + 35 + 35) / 3 = 105 / 3 ≈ 35
This solution is correct!
Solution 2:
35, 35, 35
Verification:
(35 + 35 + 35) / 3 = 105 / 3 ≈ 35
This solution is correct!
Solution 3:
95, 2, 8
Verification:
(95 + 2 + 8) / 3 = 105 / 3 ≈ 35
This solution is correct!
Solution 4:
86, 7, 12
Verification:
(86 + 7 + 12) / 3 = 105 / 3 ≈ 35
This solution is correct!
Solution 5:
19, 84, 2
Verification:
(19 + 84 + 2) / 3 = 105 / 3 ≈ 35
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 105 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.