Question

The sophomore class sold a total of $700$ adult and student tickets to the school play.

Adult tickets sold for $\$4.50$ each and student ticket cost $\$2.00$ each.

If they took in a total of $\$1200$, which system of equation can be used to find $\mathrm{x}$, the number of student tickets sold, and $\mathrm{y}$; the number of adult tickets sold $?$

• A. $$\begin{gathered} \mathrm{x}+\mathrm{y}=1200 \\ 2\mathrm{x}+4.5\mathrm{y}=700 \end{gathered}$$
• B. $$\begin{gathered} \mathrm{x}+\mathrm{y}=700 \\ 2\mathrm{x}+4.5\mathrm{y}=1200 \end{gathered}$$
• C. $$\begin{gathered} \mathrm{x}+\mathrm{y}=1200 \\ \mathrm{x}+\mathrm{y}=700 \end{gathered}$$

Answer 1

The correct option is B

$$\begin{gathered} \mathrm{x}+\mathrm{y}=700 \\ 2\mathrm{x}+4.5\mathrm{y}=1200 \end{gathered}$$

Explanation for correct option:

Option $\left(\mathbf{B}\right)$:

Find the system of equation for the number of student tickets sold and the number of adult tickets sold.

Let $\mathrm{x}$ be the number of student tickets sold and $\mathrm{y}$ be the number of adult tickets sold:

Since the total number of tickets sold by the Sophomore class were $700$:

$\mathbf{x}\mathbf{+}\mathbf{y}\mathbf{=}\mathbf{700}\mathbf{}\mathbf{}\mathbf{}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{\left(}\mathbf{1}\mathbf{\right)}$

Cost of $1$ student ticket was $\$2.00$

Then, cost of $\mathrm{x}$ students ticket will be:

$\mathrm{x}\times 2=2\mathrm{x}$

Cost of $1$ adult ticket was $\$4.50$

Then, cost of $\mathrm{y}$ adult tickets will be:

$4.5\times \mathrm{y}=4.5\mathrm{y}$

Therefore, the total cost of tickets will be as follows:

$2\mathrm{x}+4.5\mathrm{y}$

According to the problem the total cost of the tickets was $\$1200$, it follows that:

$\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{4}\mathbf{.}\mathbf{5}\mathbf{y}\mathbf{=}\mathbf{1200}\mathbf{}\mathbf{}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{\left(}\mathbf{2}\mathbf{\right)}$

Hence, the system of equations are as follows:

$\mathbf{x}\mathbf{+}\mathbf{y}\mathbf{=}\mathbf{700}$

$\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{4}\mathbf{.}\mathbf{5}\mathbf{y}\mathbf{=}\mathbf{1200}$

Hence, Option $\left(B\right)$ is the correct option.

Explanation for incorrect option:

Since the system of equations in option $\left(\mathrm{A}\right)$ is not equivalent to first and second equations above, option $\left(\mathrm{A}\right)$ is incorrect.

Since the system of equations in option $\left(\mathrm{C}\right)$ is not equivalent to first and second equations above, option $\left(\mathrm{C}\right)$ is incorrect.

Hence, Option $\left(B\right)$ is the correct option.