Brenna, a college student, offers private after-school and weekend tutoring sessions to elementary and middle school students. She schedules 30-minute sessions for elementary school students and 45-minute sessions for middle school students. Brenna wants to tutor fewer than 15 hours per week to have time for her own studies.
Which graph represents how many elementary school sessions, x, and middle school sessions, y, Brenna can schedule?
Since Brenna schedules 30-minute sessions for elementary school students and 45-minute sessions for middle school students, we can use the following equations to represent the total hours of tutoring sessions Brenna can schedule per week:
For elementary school students: 30 minutes/session x = 0.5x hours/session
For middle school students: 45 minutes/session y = 0.75y hours/session
Since Brenna wants to tutor fewer than 15 hours per week, the total hours per week can be represented as:
0.5x + 0.75y < 15
To represent this inequality on a graph, we can plot all the possible combinations of x and y that satisfy the inequality.
The graph should show x on the x-axis and y on the y-axis. The area below the line 0.5x + 0.75y = 15 represents all the possible combinations of x and y that satisfy the inequality.
Therefore, the graph that best represents how many elementary school sessions, x, and middle school sessions, y Brenna can schedule would show a shaded region below the line 0.5x + 0.75y = 15.