Answer:
[tex]\dfrac{2}{3}x \geq 250[/tex]
Step-by-step explanation:
Let x be the number of students in the senior class.
If two-thirds of the seniors bought prom tickets and a minimum number of 250 tickets needs to be sold, the inequality that models this scenario is:
[tex]\boxed{\dfrac{2}{3}x \geq 250}[/tex]
Solving the inequality:
[tex]\implies \dfrac{2}{3}x \geq 250[/tex]
[tex]\implies 2x \geq 250 \cdot 3[/tex]
[tex]\implies 2x \geq 750[/tex]
[tex]\implies x \geq 750 \div 2[/tex]
[tex]\implies x \geq 375[/tex]
Therefore, there must be at least 375 students in the senior class to ensure they sold enough tickets to keep the venue.
