The average of 10 numbers is 12. If one number is removed, the average is 11. What number is removed?
( a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 + a10 ) / 10 = 12 Multiply both sides by 10
a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 + a10 = 120
( a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 ) / 9 = 11 Multiply both sides by 9
a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 = 99
( a1 + a2 + a3 + a4 + a5 + a6 + a7 + a8 + a9 ) + a10 = 120
99 + a10 = 120 Subtract 99 to both sides
99 + a10 - 99 = 120 -99
a10 = 21
Number 21 is removed.
Well, it sounds like we have a disappearing act on our hands! So, to find out which number vanished, let's do a little math.
If the average of 10 numbers is 12, then the sum of those numbers is 10 multiplied by 12, which is 120.
Now, if after removing one number, the average becomes 11, then the sum of the remaining 9 numbers is 9 multiplied by 11, which is 99.
To figure out the missing number, we need to find the difference between the original sum (120) and the sum without the missing number (99).
So, 120 minus 99 equals... drumroll, please... 21!
Therefore, the mysterious number that was removed is 21. It must have been practicing some magic tricks behind our backs!
To solve this problem, we can use the concept of averages.
1. Let's consider the sum of the 10 numbers as "X". So, the average of these 10 numbers is X/10 = 12.
2. If we remove one number and the average becomes 11, the sum of the remaining 9 numbers would be (9 * 11) = 99.
3. Therefore, the sum of all 10 numbers can be calculated as X = (Average * Number of Elements) = (11 * 9) = 99.
4. Since the average of all 10 numbers is 12, the sum of all 10 numbers can also be calculated as X = (Average * Number of Elements) = (12 * 10) = 120.
5. Now, we can calculate the number that was removed by subtracting the sum of the remaining 9 numbers from the sum of all 10 numbers: 120 - 99 = 21.
Therefore, the number that was removed is 21.
To find the number that is removed, we need to first calculate the sum of the 10 numbers by multiplying the average by the count:
Sum of 10 numbers = average * count = 12 * 10 = 120
If we remove one number and the new average is 11, we need to find the new sum of the 9 remaining numbers.
New sum of 9 numbers = average * count = 11 * 9 = 99
The difference between the original sum and the new sum will give us the removed number:
Removed number = Sum of 10 numbers - New sum of 9 numbers
Removed number = 120 - 99 = 21
Therefore, the number that is removed is 21.
the total of the 10 number is 120
solve
(120-x)/9 = 11
120-x = 99
-x = -21
x = 21