the average of 20 numbers in a list is 32. when a number is added to the list, the average becomes 34. What number was added to the list?
so i started like this...
x/20= 32
my answer is 640. is this correct?
no
think backwards, and how "average" is obtained
the average of 20 numbers was 32, so the total of all the numbers must have been 20x32 or 640.
For 21 numbers the average was now 34, so the total must have been 21x34 or 714
so 714-640 or 74 must have been the number added
To find the number that was added to the list, we can start by setting up the equation based on the given information:
We're given that the average of 20 numbers in a list is 32, so we can express this as:
(20 numbers sum)/20 = 32
Next, we're told that when a number is added to the list, the average becomes 34. This means we now have 21 numbers in the list, so we can express this as:
(21 numbers sum)/21 = 34
To find the number added to the list, we can subtract the sum of the original 20 numbers from the sum of the 21 numbers:
(21 numbers sum) - (20 numbers sum) = (number added to the list)
Now let's calculate the sum of the original 20 numbers:
20 * 32 = 640
Now let's calculate the sum of the 21 numbers:
21 * 34 = 714
Finally, subtract the sum of the original 20 numbers from the sum of the 21 numbers to find the number added to the list:
714 - 640 = 74
Therefore, the number added to the list is 74, not 640.