Question

Tickets at a play cost $\$10$ or $\$14$.

If $800$ tickets were sold and $\$9,040$ was collected by the box office, how many $\$14$ ticket were sold $?$

Answer 1

Find the number of $\$14$ tickets sold at a play:

Let the number of $\$14$ tickets sold be $\mathrm{x}$:

Since total tickets sold were $800$, the number of $\$10$ will be:

$800-\mathrm{x}$

Cost of one $\$14$ ticket $=\$14$

Cost of $\mathrm{x}$ tickets of same price $=14\mathrm{x}$

Cost of one $\$10$ ticket $=\$10$

Cost of $800-\mathrm{x}$ tickets of same price $=10(800-\mathrm{x})$

Therefore, the total cost of tickets will be:

$$\begin{gathered} 14\mathrm{x}+10(800-\mathrm{x}) \\ =14\mathrm{x}+8000-10\mathrm{x} \\ =4\mathrm{x}+8000 \end{gathered}$$ [Add the like terms together]

Since the total cost of the tickets was $\$9,040$, it follows that:

$\begin{array}{rcl}4\mathrm{x}+8000& =& 9040\\ & \Rightarrow & 4\mathrm{x}=9040-8000\\ & \Rightarrow & \mathrm{x}=\frac{1040}{4}\end{array}$

$\therefore \mathrm{x}=260$

Hence, the the number of $\$14$ tickets sold at a play were $\mathbf{260}$.