Un hotel alquiló 108 habitaciones, dobles e individuales. El costo de habitación doble por noche es $78 y de habitación individual $72. El hotel obtuvo $7,839 de ingreso por el alquiler de las habitaciones durante una noche ¿Cuántas habitaciones dobles y cuantas habitaciones sencillas alquiló esa noche?

Question

01-02-2017
Mathematics

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Un hotel alquiló 108 habitaciones, dobles e individuales. El costo de habitación doble por noche es $78 y de habitación individual $72. El hotel obtuvo $7,839 de ingreso por el alquiler de las habitaciones durante una noche ¿Cuántas habitaciones dobles y cuantas habitaciones sencillas alquiló esa noche?

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Edufirst Edufirst · Answer 1 · 2017-02-10T12:37:03+01:00

I have to assume that you want the answer in Spanish *but without using accents).

Usa las siguientes variables:

d = numero de habitaciones dobles

i = numero de habitaciones individuales

Por la primera premisa:

d + i = 180

Por la segunda premisa, los costos son tales que:

78d + 72i = 7839

Para resolver ese sistema podemos despejar una de las variables de la primera ecucacion y sustituir en la segunda:

i = 180 - d

78d + 72 (180 - d) = 7839

78d + 12960 - 72d = 7839

De aqui ya veo que va a dar un numero negativo para el numero de habitaciones dobles, asi que supongo que algun dato en el enunciado esta equivocado.

6d = 7839 - 12960 = -5121

=> d = -5121 / 6 = - 853.5

Al corregir los datos podras seguir el procedimiento que te he explicado para encontrar la solucion.