To solve this problem, we need to use the information given and work our way through the frequency tree.
Let's start by filling in the values that we know:
The total number of tickets sold is 100.
M + Q + R + S = 100
Of these tickets, 64 are adult tickets.
Q + S = 64
23 of the child tickets sold were not premium tickets.
Q = 23 + S
19 of the total tickets sold were premium tickets.
R + S = 19
Now, let's substitute the values of Q and R using the equation Q = 23 + S:
23 + S + S = 64
2S + 23 = 64
2S = 64 - 23
2S = 41
S = 41/2
S = 20.5
Since we cannot have half of a ticket, we conclude that the value of S should be 20.
Now, substitute the value of S in the equation R + S = 19:
R + 20 = 19
R = 19 - 20
R = -1
Since we cannot have a negative number of tickets, we conclude that the value of R should be 0.
Finally, substitute the values of R and S in the equation M + Q + R + S = 100:
M + Q + 0 + 20 = 100
M + Q + 20 = 100
M + Q = 100 - 20
M + Q = 80
Therefore, M should be 80.
So, the values that should replace M and Q are 80 and 20, respectively.