Question

adult tickets for the school play cost $5 and student tickets cost $3. thirty more student tickets were sold than adult tickets. if $1770 was collected, how many of each type of ticket was sold?

Explanation:

Step1: Define variables

Let $x$ = number of adult tickets sold. Then $x+30$ = number of student tickets sold.

Step2: Set up revenue equation

Total revenue = (adult ticket price × adult tickets) + (student ticket price × student tickets)
$$5x + 3(x+30) = 1770$$

Step3: Expand and simplify equation

$$5x + 3x + 90 = 1770$$
$$8x + 90 = 1770$$

Step4: Isolate the variable term

$$8x = 1770 - 90$$
$$8x = 1680$$

Step5: Solve for $x$

$$x = \frac{1680}{8} = 210$$

Step6: Find student ticket count

Student tickets = $x+30 = 210 + 30 = 240$

Answer:

210 adult tickets and 240 student tickets were sold.