What three numbers have an average of 63?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 63. This means if we add these three numbers together and divide by 3, we should get 63.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 63 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 63 * 3 = x + y + z
- So, the sum of our three numbers should be: 189
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 189.
Solution 1:
63, 63, 63
Verification:
(63 + 63 + 63) / 3 = 189 / 3 ≈ 63
This solution is correct!
Solution 2:
63, 63, 63
Verification:
(63 + 63 + 63) / 3 = 189 / 3 ≈ 63
This solution is correct!
Solution 3:
112, 56, 21
Verification:
(112 + 56 + 21) / 3 = 189 / 3 ≈ 63
This solution is correct!
Solution 4:
89, 31, 69
Verification:
(89 + 31 + 69) / 3 = 189 / 3 ≈ 63
This solution is correct!
Solution 5:
100, 18, 71
Verification:
(100 + 18 + 71) / 3 = 189 / 3 ≈ 63
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 189 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.