Question

A student theater charges $9.50 per ticket. a. The theater has already sold 70 tickets. Identify an inequality that represents how many more tickets xx the theater needs to sell to earn at least $1000. 70+9.50x≥100070+9.50x≥1000 (9.50)(70)+x≥1000(9.50)(70)+x≥1000 9.50(70+x)≥10009.50(70+x)≥1000 1000≥(9.50)(70)+9.50x1000≥(9.50)(70)+9.50x Question 2 Solve the inequality.

Answer 1

Answer-

The inequality equation for the given problem is "9.50(70+x) ≥ 1000"

And the theater need to sell 36 more tickets in order to get at least $1000.

Solution-

Let's assume x is the number of more tickets to sell in order to get at least  $1000  and the price of one ticket is $9.50.

No. of tickets already sold by the theater = 70

So total earnings till now = $(70 × 9.50)

Total earnings by selling x tickets = $(x × 9.50)

∴ Hence, the inequality equation is,

$70\times9.50 \ + \ x \times 9.50 \geq 1000$

$\Rightarrow 9.50(70+x)\geq 1000$

$\Rightarrow 70+x\geq105.26$

$\Rightarrow x=35.26 \approx 36$  ( ∵ since tickets can only be sold as whole)

∴ So, the theater need to sell 36 more tickets in order to get at least $1000.