the members of the drama club have 100 tickets to sell to the school play. students pay $5 per ticket, and…

the members of the drama club have 100 tickets to sell to the school play. students pay $5 per ticket, and nonstudents pay $10 per ticket. the drama club needs to collect at least $800 in total ticket sales. the system of inequalities represents the number of student tickets, s, and the number of nonstudent tickets, n, the members must sell.\ns + n ≤ 100\n5s + 10n ≥ 800\nwhat is the maximum number of student tickets that can be sold if the drama club meets its sales goal?\n40\n60\n80\n100

the members of the drama club have 100 tickets to sell to the school play. students pay $5 per ticket, and nonstudents pay $10 per ticket. the drama club needs to collect at least $800 in total ticket sales. the system of inequalities represents the number of student tickets, s, and the number of nonstudent tickets, n, the members must sell.\ns + n ≤ 100\n5s + 10n ≥ 800\nwhat is the maximum number of student tickets that can be sold if the drama club meets its sales goal?\n40\n60\n80\n100

Answer

Explanation:

Step1: Express $n$ from the first - inequality

$n\leq100 - s$

Step2: Substitute $n$ into the second inequality

$5s+10n\geq800$, substituting $n$ gives $5s + 10(100 - s)\geq800$.

Step3: Expand and solve the inequality

Expand: $5s+1000 - 10s\geq800$. Combine like - terms: $- 5s\geq800 - 1000=-200$. Divide both sides by $-5$ and reverse the inequality sign: $s\leq40$.

Answer:

40