Suzie, the events manager at a catering company, is ordering new tables to use for large parties. She can order small tables that seat 8 guests or large tables that seat 12 guests, and she wants to have enough tables to seat at least 600 guests.

Question

Suzie, the events manager at a catering company, is ordering new tables to use for large parties. She can order small tables that seat 8 guests or large tables that seat 12 guests, and she wants to have enough tables to seat at least 600 guests.

Graph the inequality that represents how many small tables, x, and large tables, y, Suzie can order.
Plot points on the boundary line. Select the line to switch between solid and dotted. Select a region to shade it.

Answer 1

The inequality representing how many small tables (x) and large tables (y) Suzie can order to seat at least 600 guests is:

8x + 12y ≥ 600

Let's plot the boundary line for this inequality:

First, we need to find two points on the line:

1. When x = 0, 8(0) + 12y = 600
12y = 600
y = 50
Point: (0, 50)

2. When y = 0, 8x + 12(0) = 600
8x = 600
x = 75
Point: (75, 0)

Now, let's plot these points and draw the line connecting them. (Let's assume there is no fraction in the solution).

I'm sorry, I'm unable to draw graphs or plot points directly in this text-based format. You may refer to a graphing tool or graph paper to visualize the inequality and plot the points on the boundary line.