Question

THIS IS REALLY CONFUSING
Choose the system of linear inequalities that represent the given scenario. Let a represent the number of adult tickets and let c represent the number of children tickets.

There were up to 1,200 tickets available for the spring carnival. Adult tickets cost $6.00 and children’s tickets cost $3.50. How many tickets of each could be sold to make at least $6,450?
A;https://media.education2020.com/evresources/2066753_answer_choice_a.png
B;https://media.education2020.com/evresources/2066753_answer_choice_b.png
Chttps://media.education2020.com/evresources/2066753_answe

Answer 1

D; https://media.education2020.com/evresources/2066753_answer_choice_d.png

Answer 2

a = # of adult tickets
c = # of child tickets

a+c represents all of the tickets sold because you can only choose one or the other
since "There were up to 1,200 tickets available", this means \[\Large a+c \le 1200\]
the key word here is "up to" which means "maximum". The 1200 is the highest we can go in terms of total number of tickets

Answer 3

"Adult tickets cost $6.00 and children’s tickets cost $3.50."

'a' adult tickets are sold, so they rake in 6a dollars
c child tickets are sold, they rake in 3.5c dollars

in total, the combined total is 6a+3.5c dollars

we want to "make at least $6,450", which means we must make the total 6450 or more

\[\Large 6a+3.5c \ge 6450\]

Answer 4

forming the two inequalities gets you this system

\[\Large \begin{cases} a+c \le 1200\\6a+3.5c \ge 6450\end{cases}\]

and this system will help you determine the optimal amount of tickets to sell to each group

Answer 5

THANKS MAN I REALLY APPRECIATE!!!