What three numbers have an average of 87?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 87. This means if we add these three numbers together and divide by 3, we should get 87.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 87 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 87 * 3 = x + y + z
- So, the sum of our three numbers should be: 261
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 261.
Solution 1:
87, 87, 87
Verification:
(87 + 87 + 87) / 3 = 261 / 3 ≈ 87
This solution is correct!
Solution 2:
87, 87, 87
Verification:
(87 + 87 + 87) / 3 = 261 / 3 ≈ 87
This solution is correct!
Solution 3:
112, 113, 36
Verification:
(112 + 113 + 36) / 3 = 261 / 3 ≈ 87
This solution is correct!
Solution 4:
160, 73, 28
Verification:
(160 + 73 + 28) / 3 = 261 / 3 ≈ 87
This solution is correct!
Solution 5:
125, 16, 120
Verification:
(125 + 16 + 120) / 3 = 261 / 3 ≈ 87
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 261 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.