Question

During her shift at the museum ticket booth, Leah sold $115$ tickets for a total of $\backslash (1,163$. Adult tickets cost $\backslash )12$ and student tickets cost $\$5$. How many adult tickets and how many student tickets did Leah sell?

Short answer

Leah sold $84$adult tickets and$31$ student tickets.

Step-by-step solution

Step 1. Given information.

Consider the given question,

Total cost of tickets sold is$\$1163$.

Cost of adult tickets is $\$12$and student tickets is $\$5$.

We know the total number of tickets sold was $115$tickets. This means the number of student’s tickets plus the number of adult tickets must add up to localid="1647176732277" $115$.

Assume xto be the number of student's ticket. Then,

localid="1647176735201" $115-x=$number of adult tickets.

Make the table,

Step 2. Form the equation.

Consider the table, we can say,

$$\begin{gathered} 5x+12\left(115-x\right)=1163 \\ 5x+1380-12x=1163 \\ 7x=217 \\ x=31 \end{gathered}$$

Then,

$$\begin{gathered} =115-31 \\ =84 \end{gathered}$$

Therefore, Leah sold $31$student's tickets and $84$adult's tickets.