Question

The drama club is putting on a production of "Noli Me Tangere" and is charging ₱150 for a student ticket and ₱200 for an adult ticket. On opening night, they made ₱15900 from 100 audience members. How many of each type of ticket did they sell?

(a) Represent the unknowns:

(b) Formulate the system of equations:

(c) Solve the system of equations:

(d) Check the solutions:

(e) State the answer:

Answer 1

The drama club sold 82 student tickets and 18 adult tickets.

Step-by-step explanation:

(a) Represent the unknowns:

Let x be the number of student tickets sold.

Let y be the number of adult tickets sold.

(b) Formulate the system of equations:

The total number of tickets sold is 100, so we have the equation:

x + y = 100

The total amount of money made is ₱15900, so we have the equation:

150x + 200y = 15900

(c) Solve the system of equations:

To solve the system of equations, we can use the method of substitution or the method of elimination. Let's use the method of substitution:

From the first equation, we have y = 100 - x. Substituting this into the second equation:

150x + 200(100 - x) = 15900

Simplifying the equation gives:

150x + 20000 - 200x = 15900

-50x = -4100

x = 82

Substituting x = 82 into the first equation gives:

82 + y = 100

y = 18

(d) Check the solutions:

Multiplying the number of student tickets by ₱150 and the number of adult tickets by ₱200, we get:

82 * 150 + 18 * 200 = 15900

So the solutions satisfy the given information.

(e) State the answer:

The drama club sold 82 student tickets and 18 adult tickets.