Question

# A drama club plans to sell 100 tickets to a school musical. An adult ticket costs $6, and a student ticket costs$4. Students who attend the school get a \$1 discount. The club expects two thirds of the student tickets to be discounted. Write an equation that gives the total revenue r (in dollars) as a function of the number a of adult tickets sold.

Solution

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Let $a$ be the number of adult ticket sold and $r$ the total revenue.

An adult ticket costs $\6$. Therefore, revenue from adult tickets is $\color{Brown}\6a$.

Since drama club has $100$ tickets to sell, number of students tickets will be $100-a$.

Student ticket costs $\4$. Since students who attend the school get $\1$ discount, their ticket costs $\3$.

Two thirds of the student tickets will be discounted. Therefore, revenue from discounted student tickets will be

$\color{Brown}\3\cdot \dfrac{2}{3} \cdot (100-a)$

$\3$ is cost of the student ticket with discount, and $\dfrac{2}{3}\cdot (100-a)$ is a number of students with discount.

Since wo thirds of the student tickets will be discounted, one third will not. ($1-\frac{2}{3}={1}{3}$) Therefore, revenue from discounted student tickets will be

$\color{Brown}\4\cdot \dfrac{1}{3} \cdot (100-a)$

$\4$ is cost of the student ticket without discount, and $\dfrac{1}{3}\cdot (100-a)$ is a number of students without discount.

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