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:
159, 68, 34
Verification:
(159 + 68 + 34) / 3 = 261 / 3 ≈ 87
This solution is correct!
Solution 4:
145, 84, 32
Verification:
(145 + 84 + 32) / 3 = 261 / 3 ≈ 87
This solution is correct!
Solution 5:
121, 99, 41
Verification:
(121 + 99 + 41) / 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.