What three numbers have an average of 722?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 722. This means if we add these three numbers together and divide by 3, we should get 722.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 722 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 722 * 3 = x + y + z
- So, the sum of our three numbers should be: 2166
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2166.
Solution 1:
722, 722, 722
Verification:
(722 + 722 + 722) / 3 = 2166 / 3 ≈ 722
This solution is correct!
Solution 2:
722, 722, 722
Verification:
(722 + 722 + 722) / 3 = 2166 / 3 ≈ 722
This solution is correct!
Solution 3:
1910, 109, 147
Verification:
(1910 + 109 + 147) / 3 = 2166 / 3 ≈ 722
This solution is correct!
Solution 4:
144, 1172, 850
Verification:
(144 + 1172 + 850) / 3 = 2166 / 3 ≈ 722
This solution is correct!
Solution 5:
220, 740, 1206
Verification:
(220 + 740 + 1206) / 3 = 2166 / 3 ≈ 722
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 2166 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.