Amy's restaurant has a budgeted at most $60 to spend this month on gourmet coffee. All international blends cost $8.50 per package and all house blends cost $6.00 per package. She would like to purchase some international blends and at least 3 packages of the house blends.

Amy's restaurant has a budget at most $60 to spend this month on gourmet coffee. All international blends cost $8.50 per package and all house blends cost $6.00 per package. She would like to purchase some international blends and at least 3 packages of the house blends. Write a system of linear inequalities that describe this situation.

Let x represent number of international blends and y represent number of house blends.

The cost of x international blends would be [tex]8.50x[/tex] and cost of y house blends would be [tex]6.00y[/tex].

Since Amy's restaurant has a budget at most $60 to spend this month on gourmet coffee, so cost of x international blends and y house blends should be less than or equal to 60.

We can represent this information in an inequality as:

[tex]8.50x+6.00y\leq 60[/tex]

Since Amelia wants to purchase at least 3 packages of the house blends, so y should be greater than or equal to 3. We can represent this information in an inequality as:

[tex]y\geq 3[/tex]

Therefore, our required system of inequalities would be [tex]8.50x+6.00y\leq 60[/tex] and [tex]y\geq 3[/tex].