The drama club is selling tickets to their play to raise money for the show’s expenses. Each student ticket sells for $6.50 and each adult ticket sells for $10. The auditorium can hold no more than 140 people. The drama club must make at least $1100 from ticket sales to cover the show’s costs. If xx represents the number of student tickets sold and yy represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.

dramaclub is selling tickets to their play to raisemoneyfor the show’sexpenses. One solution is the place where the two lines cross, which reflects the minimal number of student and adult tickets needed to achieve the minimum ticket revenue criterion. This point resolves theinequality system.## What is the solution to a system of inequalities?

inequalities, we need to represent the two conditions that must be satisfied: the total number of tickets sold must be less than or equal to 140 and the total ticket revenue must be at least $1100.total numberof tickets sold. Since each student ticket sells for $6.50 and each adult ticket sells for $10, the total number of student tickets sold is 6.50xx and the total number of adult tickets sold is 10yy. Therefore, the total number of tickets sold is 6.50xx + 10yy. We can express this as aninequalityas follows:total ticket revenue. Since each student ticket sells for $6.50 and each adult ticket sells for $10, the total revenue from student ticket sales is 6.50xx and the total revenue from adult ticket sales is 10yy. Therefore, the total ticket revenue is 6.50xx + 10yy. We can express this as an inequality as follows:inequalities:inequalitiesgraphically, we can plot the two inequalities on the samecoordinateplane and find the region of the plane that satisfies both inequalities.inequality, 6.50xx + 10yy ≤ 140, we can solve for yy in terms of xx by dividing both sides of the inequality by 10:equationfor a line with slope -6.5 and y-intercept 14. To graph this inequality, we can plot the line and shade the region above the line.equationfor a line with slope -6.5 and y-intercept 110. To graph this inequality, we can plot the line and shade the region below the line.inequalitiesis the intersection of the two shaded regions. This is the area where the number of student tickets and the number of adult tickets can be varied to satisfy both conditions.inequalities.systemofinequalities