Respuesta :
Answer:
150 adult tickets, 80 student ticket and 48 senior tickets.
Step-by-step explanation:
Given:
A theater has tickets priced at $6 for adults, $3.50 for students, and $2.50 for seniors.
A total of 278 tickets were sold for one showing with a total revenue of 1300.
If the number of adult tickets sold was 10 less than twice the numbers of student tickets.
Question asked:
How many of each type of ticket were sold?
Solution:
Let the number of students tickets sold = [tex]x[/tex]
Then the number of adult tickets sold = [tex]2x-10[/tex]
Then the number of senior tickets sold =
[tex]278-(x+2x-10)=278-(3x-10)=278-3x+10=288-3x[/tex]
Total revenue = $1300
[tex]3.5\times x+6(2x-10)+2.5(288-3x)=1300\\ \\ 3.5x+12x-60+720-7.5x=1300\\ \\ 8x+660=1300\\ \\ Subtracting\ both\ sides\ by\ 660\\ \\ 8x=640\\ \\ Dividing\ both\ sides\ by\ 8\\ \\ x=80[/tex]
The number of students tickets sold = [tex]x[/tex] = 80
The number of adult tickets sold = [tex]2x-10[/tex] = [tex]2\times80-10=160-10=150[/tex]
The number of senior tickets sold = [tex]288-3x=288-3\times80=288-240=48[/tex]
Therefore, 150 adult tickets, 80 student ticket and 48 senior tickets are sold.
