Question

Mason is working two summer jobs, making $7 per hour babysitting and making $10 per hour clearing tables. In a given week, he can work at most 12 total hours and must earn no less than $90. If xx represents the number of hours babysitting and yy represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.

Answer 1

Answer: We know that:

x + y = 12 (because he can work at most 12 hours in total)

7x + 10y ≥ 90 (because he must earn no less than $90)

We can graph these inequalities on the coordinate plane.

The equation x + y = 12 represents a line with a slope of -1 and y-intercept of 12. This is the line that separates the region where he works more hours babysitting and the region where he works more hours clearing tables.

The inequality 7x + 10y ≥ 90 represents the region where he earns more than $90.

You can find the solution by finding the intersection of the line and the shaded region. The solution will be a point that lies on both the line and the shaded region.

One possible solution would be for Mason to work 8 hours babysitting and 4 hours clearing tables, earning him $56 from babysitting and $40 from clearing tables, for a total of $96.

Explanation: