What three numbers have an average of 770?
Part 1: Understanding the Problem
We're looking for three numbers whose average is 770. This means if we add these three numbers together and divide by 3, we should get 770.
Step-by-step Solution:
- Recall the average formula: Average = (Sum of numbers) / (Count of numbers)
- In this case: 770 = (x + y + z) / 3
- To find the sum, multiply both sides by 3: 770 * 3 = x + y + z
- So, the sum of our three numbers should be: 2310
Part 2: Finding Solutions
Now, let's find multiple sets of three numbers that add up to 2310.
Solution 1:
770, 770, 770
Verification:
(770 + 770 + 770) / 3 = 2310 / 3 ≈ 770
This solution is correct!
Solution 2:
770, 770, 770
Verification:
(770 + 770 + 770) / 3 = 2310 / 3 ≈ 770
This solution is correct!
Solution 3:
1114, 389, 807
Verification:
(1114 + 389 + 807) / 3 = 2310 / 3 ≈ 770
This solution is correct!
Solution 4:
1207, 467, 636
Verification:
(1207 + 467 + 636) / 3 = 2310 / 3 ≈ 770
This solution is correct!
Solution 5:
985, 122, 1203
Verification:
(985 + 122 + 1203) / 3 = 2310 / 3 ≈ 770
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 2310 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.