What three numbers have an average of 498?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 498. This means if we add these three numbers together and divide by 3, we should get 498.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 498 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 498 * 3 = x + y + z
- So, the sum of our three numbers should be: 1494
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 1494.
Solution 1:
498, 498, 498
Verification:
(498 + 498 + 498) / 3 = 1494 / 3 ≈ 498
This solution is correct!
Solution 2:
498, 498, 498
Verification:
(498 + 498 + 498) / 3 = 1494 / 3 ≈ 498
This solution is correct!
Solution 3:
1166, 166, 162
Verification:
(1166 + 166 + 162) / 3 = 1494 / 3 ≈ 498
This solution is correct!
Solution 4:
158, 507, 829
Verification:
(158 + 507 + 829) / 3 = 1494 / 3 ≈ 498
This solution is correct!
Solution 5:
1313, 110, 71
Verification:
(1313 + 110 + 71) / 3 = 1494 / 3 ≈ 498
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 1494 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.