Question

La dirección del Colegio Montes y los padres de familia están organizando un viaje cultural a Guanajuato para los alumnos de segundo y sus profesores. Los alumnos dormirán en cuartos dobles y los profesores en sencillos. El hotel tiene habitaciones dobles (2camas) y sencillas (1 cama), sumando en total 47 habitaciones y 79 camas. Para confirmar si se pueden acomodar, quieren saber cuantas habitaciones hay de cada tipo. Si "x" denota las habitaciones sencillas y "y" las dobles, escribe el sistema de ecuaciones que representa la situación: Ecuación que representa el número de habitaciones (1) Ecuación que representa el número de camas (2)

Answer 1

x + y = 47 (eqn 1)

x + 2y = 79 (eqn 2)

Solving the simultaneous equation,

The hotel has 15 single rooms and 32 double rooms.

Explanation:

English Translation

The management of Colegio Montes and the parents are organizing a cultural trip to Guanajuato for second grade students and their teachers. Students will sleep in double rooms and teachers in singles. The hotel has double rooms (2 beds) and single rooms (1 bed), totaling 47 rooms and 79 beds. To confirm if they can be accommodated, they want to know how many rooms there are of each type. If "x" denotes single rooms and "y" denotes double rooms, Write the system of equations that represents the situation: Equation that represents the number of rooms (1) Equation that represents the number of beds (2)

Solution

The number of single rooms = x

The number of double rooms = y

The number of beds in single rooms = x

The number of beds in double rooms = 2y

Total number of rooms = 47

Total number of beds = 79

Sum of single and double rooms = Total number of rooms

x + y = 47 (eqn 1)

Sum of the beds in the single rooms and the beds in the double rooms = Total number of beds

x + 2y = 79 (eqn 2)

Writing the equations together

x + y = 47 (eqn 1)

x + 2y = 79 (eqn 2)

Solving the equations simultaneously,

x = 15, y = 32

Hence, the hotel has 15 single rooms and 32 double rooms.

Hope this Helps!!!