An arena sold 100 tickets for a concert, of which 64 are adult tickets.
The rest were child tickets.
23 of the child tickets sold were not premium tickets.
19 of the total tickets sold were premium tickets.
By copying and completing the frequency tree below, work out the values that should replace M and Q.
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.