Gianna is preparing for the upcoming tennis season. According to her schedule, she can complete at most 10 workouts this week. It takes Gianna 45 minutes to complete her drill-based workouts and 30 minutes to complete her conditioning workouts. She is required to spend more than 450 minutes on workouts every week.Which system of inequalities can be used to determine the number of drill-based workouts, x, and the number of conditioning workouts, y, that Gianna can complete this week?

The whole number of minutes that Gianna complete each week as a function of x and y:
[tex]45x+30y[/tex]
Since the above number is greater than 450 minutes, we get the inequality:
[tex]45x+30y\geq450[/tex]
Also, "she can complete at most 10 workouts this week" so we deduce the inequality:
[tex]\\x+y\leq10[/tex]
Therefore, the system of inequalities is the following:
[tex]45x+30y\geq450[/tex]
[tex]\\x+y\leq10[/tex]
The above system has many solutions, for example :