Question

A student theater charges $\$8.50$ per ticket.
(A). The theater has already sold $70$ tickets. How many more tickets does the theater need to sell to earn at least $\$750$?
(B). The theater increases the ticket price by $\$1$. Without solving an inequality, describe how this aspects the total number of tickets needed to earn at least$\$750$. Explain your r

Answer 1

Step 1: finding the total earn by the theater

We have,

A student theater charges$\$8.50$ per ticket.

The number of additional tickets sold $=x$
Then the total number of tickets sold $=x+70$
as given Each ticket cost is $\$8.50$

Then total earn by theater $=8.50(x+70)$
As the theater wants to earn at least $\$750$

Step 2 : Solve the inequality

We have,

the required inequality is:

$\mathbf{\Rightarrow }\mathbf{}8.50(x+70)\ge 750$

$\Rightarrow (x+70)\ge \frac{750}{8.50}$ [ Divide by $8.50$both sides ]
$\Rightarrow x+70\ge 88.23$

$\Rightarrow x\ge 88.23–70$ [ Subtract $70$ from both sides ]
$\therefore x\ge 18.235$
Hence, $18$ more tickets needed.

Solution (b).

If the theater charges more per ticket,

Then they needed less number of tickets to reach their goal $\$750$.