What three numbers have an average of 672?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 672. This means if we add these three numbers together and divide by 3, we should get 672.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 672 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 672 * 3 = x + y + z
- So, the sum of our three numbers should be: 2016
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2016.
Solution 1:
672, 672, 672
Verification:
(672 + 672 + 672) / 3 = 2016 / 3 ≈ 672
This solution is correct!
Solution 2:
672, 672, 672
Verification:
(672 + 672 + 672) / 3 = 2016 / 3 ≈ 672
This solution is correct!
Solution 3:
801, 123, 1092
Verification:
(801 + 123 + 1092) / 3 = 2016 / 3 ≈ 672
This solution is correct!
Solution 4:
1887, 30, 99
Verification:
(1887 + 30 + 99) / 3 = 2016 / 3 ≈ 672
This solution is correct!
Solution 5:
1748, 49, 219
Verification:
(1748 + 49 + 219) / 3 = 2016 / 3 ≈ 672
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 2016 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.