What three numbers have an average of 290?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 290. This means if we add these three numbers together and divide by 3, we should get 290.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 290 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 290 * 3 = x + y + z
- So, the sum of our three numbers should be: 870
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 870.
Solution 1:
290, 290, 290
Verification:
(290 + 290 + 290) / 3 = 870 / 3 ≈ 290
This solution is correct!
Solution 2:
290, 290, 290
Verification:
(290 + 290 + 290) / 3 = 870 / 3 ≈ 290
This solution is correct!
Solution 3:
583, 274, 13
Verification:
(583 + 274 + 13) / 3 = 870 / 3 ≈ 290
This solution is correct!
Solution 4:
594, 110, 166
Verification:
(594 + 110 + 166) / 3 = 870 / 3 ≈ 290
This solution is correct!
Solution 5:
180, 374, 316
Verification:
(180 + 374 + 316) / 3 = 870 / 3 ≈ 290
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 870 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.