A set of 7 numbers has a mean of 9. What

additional number must be included in this set to create a new set with a mean that is 3 less than the mean of the original set?

(7(9) + x)/8 = 6

63 + x = 48
x = -15

So you would have to add a negative number ?

I do not know the answer to this problem but, I am having trouble understanding it. You see, if you multiply 7x9 and get 63, other sources are saying to multiply 6x8 after and I have no clue why, where did the 8 come from?

To solve this problem, we need to find the mean of the new set and then determine the additional number that would result in a mean 3 less than the mean of the original set.

Step 1: Find the sum of the original set.
The mean of a set of numbers is the sum of the numbers divided by the count of numbers. In this case, the mean of the original set is 9. Given that the set has 7 numbers, the sum of the original set is 9 x 7 = 63.

Step 2: Find the sum of the new set.
To find the sum of the new set, we need to determine the number of elements in the new set. Since we are adding one additional number to the original set, the new set will have a count of 8.
Given that the mean of the new set is 3 less than the mean of the original set, we can calculate the sum of the new set by using the formula:
sum of new set = (mean of new set - 3) x count of elements in the new set.

Let's calculate the sum of the new set: sum of new set = (9 - 3) x 8 = 6 x 8 = 48.

Step 3: Determine the additional number.
The additional number that must be included in the set to create a new set with a mean that is 3 less than the mean of the original set can be calculated by subtracting the sum of the original set from the sum of the new set.

additional number = sum of new set - sum of original set = 48 - 63 = -15.

Therefore, the additional number that must be included in the original set to create a new set with a mean that is 3 less than the mean of the original set is -15.

To solve this problem, we first need to find the mean of the original set.

Since the mean is the sum of all the numbers divided by the total count, we know that the sum of the original set is 7 * 9 = 63.

Now, let's call the additional number we need to include in the set "x".

To find the mean of the new set, we need to consider that the new mean is 3 less than the original mean, which means it is 9 - 3 = 6.

To calculate the sum of the new set, we need to add the sum of the original set (63) to the additional number (x). Therefore, the sum of the new set is 63 + x.

We can now set up an equation to solve for x:

(63 + x) / (7 + 1) = 6

Simplifying the equation, we have:

(63 + x) / 8 = 6

Multiplying both sides of the equation by 8, we get:

63 + x = 48

Subtracting 63 from both sides of the equation, we find:

x = 48 - 63 = -15

Therefore, the additional number that must be included in the set to create a new set with a mean that is 3 less than the mean of the original set is -15.