The mean of a set of twelve numbers is 5.5. The mean of another set of eight numbers is k. The mean of the combined set of 20 numbers is 8.5. Find the value of k

total of 1st set is 12*5.5

total of 2nd set is 8k
total of two sets is 20*8.5

so, you have

12*5.5 + 8k = 20*8.5
k = 13

To find the value of k, we need to use the information given about the means of the two sets and the combined set.

Let's start with the first set of twelve numbers whose mean is 5.5. We know that the sum of these twelve numbers is equal to 12 multiplied by the mean:

Sum of the first set = 5.5 * 12 = 66

Now, let's move on to the second set of eight numbers. We are given that the mean of this set is k. Therefore, the sum of these eight numbers is equal to 8 multiplied by k:

Sum of the second set = k * 8

Finally, we are also given that the mean of the combined set of twenty numbers is 8.5. Using the same logic as before, we can find the sum of all twenty numbers:

Sum of the combined set = 8.5 * 20 = 170

Now, we can use this information to form an equation:

Sum of the first set + Sum of the second set = Sum of the combined set

66 + k * 8 = 170

Now, let's solve this equation to find the value of k:

66 + 8k = 170
8k = 170 - 66
8k = 104
k = 104/8
k = 13

Therefore, the value of k is 13.