Question

1. **Gabriella and Lisbet are selling bracelets and earrings to make money for their summer vacation. The bracelets will cost $2 and earrings will cost $3. They want to make at least $500 and would like to make less than 50 bracelets to make a profit. Graph the solution set to the system of linear inequalities in the coordinate plane below. Label your axes and create a scale. a. Is it possible for Gabriella and Lisbet to make a profit? Justify your answer using your graph above.

Answer 1

It is possible for Gabriella and Lisbet to make a profit

Step-by-step explanation:

Let's call x the number of bracelets that they will make and y the number of earrings that they will make.

If the bracelets will cost $2 and the earring will cost $3, they will make:

2x + 3y

Then, this quantity should be at least $500, so:

2x + 3y ≥ 500

Additionally, they would like to make less than 50 bracelets, so:

x < 50

So, the system of inequalities is:

2x + 3y ≥ 500

x < 50

Now, to graph the system, we need to identify the lines that separate the regions. So, for x < 50, we get that the line is x = 50, a vertical line that passes through the point (0, 50).

For 2x + 3y ≥ 500, we need to identify two points that belong to the line

2x + 3y = 500 as (250, 0) and (100, 100)

So, the graph of the inequalities is:

Therefore, the solution of the system is the yellow region. Since there is a region in the graph, Gabriella and Lisbet can make a profit.