Question

The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $6 and each adult ticket sells for $11. The auditorium can hold at most 100 people. The drama club must make no less than $770 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.

Answer 1

Im not really sure what the question is asking but the drama club could sell 70 adult tickes and 30 student tickes and they would make $950.

Explanation:

Answer 2

possible solution (10,80)

Explanation:

Variable Definitions:

x=the number of student tickets sold

y= the number of adult tickets sold

“at most 100 people"→100 or fewer tickets

Therefore the total number of tickets sold, x+y, must be less than or equal to 100:

x+y≤100

“no less than $770"→$770 or more

Each student ticket sells for $6, so x student tickets will bring in 6x dollars. Each adult ticket sells for $11, so y adult tickets will bring in 11y dollars. Therefore, the total amount of revenue 6x+11y must be greater than or equal to $770:

6x+11y≥770

Solve each inequality for y:

x+y≤100

y≤−x+100

6x+11y≥770

11y≥770−6x

y≥ -6/11x+70

Graph y≤100−x by shading down and graph y≥-6/11x+70

by shading up