Question

Para el concierto de inicio de clase Se vendieron un total de 150 boletos. el costo del boleto fue de $5.00 para estudiantes y de $8.00 a los invitados. si los ingresos totales por concepto de la venta de boletos fueron de $930.00 Entonces cuántos boletos se vendieron de cada categoría?

​

Answer 1

x + y = 150

5x + 8y = 930

y = -x + 150

5x + 8(-x + 150) = 930

5x - 8x + 1200 = 930

-3x = -270

x = 90

90 + y = 150

y = 60

90 boletas para estudiantes y 60 a los invitados vendieron

Answer 2

The number of tickets that were sold in each category include;

x = 90 student tickets.

y = 60 guest tickets.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of student tickets and guest tickets, and then translate the word problem into a linear equation as follows:

• Let the variable x represent the number of student tickets.
• Let the variable y represent the number of guest tickets.

Based on the information provided about the class concert, a system of linear equations that models the situation can be written as follows;

x + y = 150 .......equation 1.

5x + 8y = 930 .......equation 2.

By isolating y in equation 1, we have;

y = -x + 150 .......equation 3.

Next, we would substitute equation 3 into equation 2 as follows;

5x + 8(-x + 150) = 930

5x - 8x + 1200 = 930

-3x = -270

x = -270/-3

x = 90 student tickets.

For the value of y, we have;

y = -x + 150

y = -90 + 150

y = 60 guest tickets.

Complete Question;

For the beginning of class concert, a total of 150 tickets were sold. The ticket cost was $5.00 for students and $8.00 for guests. If the total revenue from ticket sales was $930.00, then how many tickets were sold in each category?