Question

A Dinner Theatre actress is paid $250 per day to rehearse the play and

$500 per day to perform in front of an audience. In one season, an
actress earned between $2000 and $5000.
Write a system of inequalities
Graph it
And give two points

Answer 1

See below

Explanation:

Let the number of days the actress rehearse d the play be x and the number of days she performed in front of an audience.

Then she earned:

• 250x + 500y

The inequalities as per minimum and maximum amount the actress earned:

• 250x + 500y > 2000 ⇒ x + 2y > 8
• and
• 250x + 500y < 5000 ⇒ x + 2y < 20

So the system is:

• x + 2y > 8
• x + 2y < 20

The graph is attached, shaded region in the middle is the solution area.

The two points shown on the graph: (5, 5) and (8, 4)