Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Given
A local theater sold 187 tickets to a matinee play with a total revenue of $1,452.00 where they changed $11.00 for adult ticket and $6.00 for a child’s ticket.
Use the variables a and c to represent the number of adult tickets sold and the number of children’s tickets sold respectively.
To determine a system of equations that describes the solution.
1) Enter the equations below separated by a comma.
2) How many adult tickets were sold?
3) How many children’s tickets were sold?
Explanation:
It is given that,
The total number of tickets sold is 187.
The total revenue is $1,452.00.
Since a and c represent the number of adult tickets sold and the number of children’s tickets sold respectively.
Then,
[tex]\begin{gathered} a+c=187\text{ \_\_\_\_\_\_\_\lparen1\rparen} \\ 11a+6c=1452\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]Solving (1) and (2) implies,
[tex]\begin{gathered} a=187-c \\ \Rightarrow11(187-c)+6c=1452 \\ \Rightarrow2057-11c+6c=1452 \\ \Rightarrow-5c=1452-2057 \\ \Rightarrow-5c=-605 \\ \Rightarrow c=\frac{605}{5} \\ \Rightarrow c=121 \end{gathered}[/tex]That implies,
[tex]\begin{gathered} a=187-c \\ a=187-121 \\ a=66 \end{gathered}[/tex]Therefore,
1) The equations are,
[tex]a+c=187,11a+6c=1452[/tex]2) The number of adults ticket sold is 66.
3) The number of Children's ticket sold is 121.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
