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.
Can Suzie order 30 small tables and 30 large tables?
a. yes
b. no
The inequality representing this situation is:
8x + 12y ≥ 600
To graph this inequality, we need to plot the boundary line 8x + 12y = 600 and shade the region above or on the line.
When we plot the points on the boundary line, we get:
(0, 50) and (75, 0)
So, the boundary line will pass through these two points.
Now, if Suzie orders 30 small tables (x = 30) and 30 large tables (y = 30), the total number of guests she can seat would be:
8(30) + 12(30) = 240 + 360 = 600
Since this total number of guests meets the requirement, she can indeed order 30 small tables and 30 large tables. So, the answer is: a. yes.