What three numbers have an average of 291?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 291. This means if we add these three numbers together and divide by 3, we should get 291.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 291 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 291 * 3 = x + y + z
- So, the sum of our three numbers should be: 873
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 873.
Solution 1:
291, 291, 291
Verification:
(291 + 291 + 291) / 3 = 873 / 3 ≈ 291
This solution is correct!
Solution 2:
291, 291, 291
Verification:
(291 + 291 + 291) / 3 = 873 / 3 ≈ 291
This solution is correct!
Solution 3:
589, 124, 160
Verification:
(589 + 124 + 160) / 3 = 873 / 3 ≈ 291
This solution is correct!
Solution 4:
150, 565, 158
Verification:
(150 + 565 + 158) / 3 = 873 / 3 ≈ 291
This solution is correct!
Solution 5:
861, 3, 9
Verification:
(861 + 3 + 9) / 3 = 873 / 3 ≈ 291
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 873 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.