Question

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 twenty numbers is 8.5. Find the value of k.

Can you please help me

Answer 1

k= 13.

You do (8.5 X 20) - (5.5 X 12), which is equal to 170 - 66 = 104
104 divided by 8 equals 13

Answer 2

mean is (sum of the values of the numbers in the set)/(how many numbers are in the set)


first bit
mean of 12 numbers is 5.5 is the same as
(12 numbers)/12=5.5

the second bit
mean of 8 numbers is k
(8 numbers)/8=k

(12numbres+8numbers)/20=8.5

interesting
one way is to solve the first and second equations for 12numbers and 8numbers

(12numbers)/12=5.5
times 12 both sides
12numbers=66

(8numbers)/8=k
multiply 8 both sides
8numbers=8k
input

(66+8k)/20=8.5
mulitply both sides by 20
66+8k=170
minus 66 both sides
8k=104
divide 8 both sides
k=13


k=13