What three numbers have an average of 53?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 53. This means if we add these three numbers together and divide by 3, we should get 53.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 53 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 53 * 3 = x + y + z
- So, the sum of our three numbers should be: 159
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 159.
Solution 1:
53, 53, 53
Verification:
(53 + 53 + 53) / 3 = 159 / 3 ≈ 53
This solution is correct!
Solution 2:
53, 53, 53
Verification:
(53 + 53 + 53) / 3 = 159 / 3 ≈ 53
This solution is correct!
Solution 3:
18, 72, 69
Verification:
(18 + 72 + 69) / 3 = 159 / 3 ≈ 53
This solution is correct!
Solution 4:
17, 134, 8
Verification:
(17 + 134 + 8) / 3 = 159 / 3 ≈ 53
This solution is correct!
Solution 5:
35, 63, 61
Verification:
(35 + 63 + 61) / 3 = 159 / 3 ≈ 53
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 159 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.