Respuesta :
Answer:
The number tickets sold was 120 student tickets, 95 children tickets and 285 adult tickets.
Step-by-step explanation:
Given:
A local theater sell all 500 tickets for a total of $8,070.
The price of tickets were $15 for students, $12 for children, and $18 for adults.
The adult tickets sold were three times as many as children’s tickets.
Now, to find the number of student tickets, children tickets and adult tickets sold.
Let the number of students ticket be [tex]x.[/tex]
Let the number of children ticket be [tex]y.[/tex]
So, the number of adults ticket be [tex]3y.[/tex]
Now, the total number of tickets sold:
[tex]x+y+3y=500\\\\x+4y=500\\\\x=500-4y\ \ \ ...(1)[/tex]
Now, the total cost of tickets:
[tex]x(15)+y(12)+3y(18)=8070\\\\15x+12y+54y=8070\\\\15x+66y=8070\\\\Substituting\ the\ value\ of\ x\ from\ equation\ (1):\\\\15(500-4y)+66y=8070\\\\7500-60y+66y=8070\\\\7500+6y=8070\\\\Subtracting\ both\ sides\ by\ 7500\ we\ get:\\\\6y=570\\\\Dividing\ both\ sides\ by\ 6\ we\ get:\\\\y=95.[/tex]
Thus, the number of children ticket is 95.
According the adult tickets sold were three times as many as children’s tickets.
Therefore, the number of adult tickets = 95 × 3 = 285.
Now, substituting the value of [tex]x[/tex] in equation (1) to get the number of student tickets:
[tex]x=500-4y\\\\x=500-4(95)\\\\x=500-380\\\\x=120.[/tex]
Hence, the number of student tickets is 120.
Therefore, the number tickets sold was 120 student tickets, 95 children tickets and 285 adult tickets.
