Question

Tickets for a school talent show cost 2$forstudentsand$ $3$ for adults. If Chris spends at least 11$butnomorethan$ $14$ on $x$ student tickets and $1$ adult ticket, what is one possible value of $x$?

• A. $4$ or $5$
• B. $3$ or $4$
• C. $2$ or $3$
• D. $5$ or $6$

Answer 1

The correct option is A $4$ or $5$

The correct answer is either $4$ or $5$. Because each student ticket costs $\$2$ and each adult ticket costs $\$3$, the total amount, in dollars, that Chris spends on $x$ student tickets and $1$ adult ticket is $2x+3$.

Because Chris spends at least $\$11$ but no more than $\$14$ on the tickets, one can write the complete inequality $2x+3\ge 1$.

Subtracting $3$ from each side of both inequalities and then dividing each side of both inequalities by $2$ yields $x\ge 4$ and $x\le 5.5$.

Thus, the value of $x$ must be an integer that is both greater than or equal to $4$ and less than or equal to $5.5$.

Therefore, $x=4$ or $x=5$.