Question

10.

Answer 1

A. To answer this question, we must consider two inequalities. The first inequality we will construct is regarding the number of tickets sold with respect to capacity. The theater cannot exceed the allotted 200 seats, so this would indicate we would use a less than or equal to inequality. The inequality we would construct to illustrate this using adult and child tickets is x + y <= 200.
The second inequality we will construct is based upon the ticket prices set and the theater’s goal. The problem indicates the theater wants to sell “at least $1,500 worth of tickets...” To create the inequality here, we will create it as follows: 12.5x + 6.25y >= 1,500.
To find the intersection point, we must isolate y. In order to do this, move x to the other side of both inequalities. Inequality 2 can be simplified to y >= -12.5x / 6.25 + 1,500 / 6.25. Graph and identify the solution from there.