Respuesta :
Let:
• The number of adult tickets sold = a;
,• The number of children’s tickets sold = c
The local theater sold 182 tickets, therefore:
[tex]a+c=182\cdots(1)[/tex]• They charged ,$21.00 for an adult ticket, and ,$11.00 for a child’s ticket,.
,• The total revenue = $2,662.00
[tex]\implies21a+11c=2662\cdots(2)[/tex](a)The system of equations is:
[tex]\begin{gathered} a+c=182\cdots(1) \\ 21a+11c=2662\cdots(2) \end{gathered}[/tex](b)
Next, we solve for the number of adult tickets sold.
From equation (1): c=182-a
Substitute c=182-a into equation (2).
[tex]\begin{gathered} 21a+11c=2662 \\ 21a+11(182-a)=2662 \end{gathered}[/tex]Solve the equation for a.
[tex]\begin{gathered} 21a+2002-11a=2662 \\ 21a-11a=2662-2002 \\ 10a=660 \\ a=\frac{660}{10} \\ a=66 \end{gathered}[/tex]66 adult tickets were sold.
(c)Finally, we find out how many children's tickets were sold.
Recall: c=182-a
[tex]c=182-a=182-66=116[/tex]116 children's tickets were sold.
Answer:
• (A) a+c=182, 21a+11c=2662
,• (B)a=66
,• (C)c=116
