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En el cuadro medallero de las útimas olim-
piadas escolares se observó que 3 estudian-
tes obtuvieron las tres medallas, 5 obtuvie-
ron medallas de oro y bronce, I estudiante
obtuvo solo medalla de oro y plata, 5 ob-
tuvieron solo medalla de bronce y 3 obtu-
vieron solo medalla de oro. Si el número de
estudiantes que solo ganaron medalla de
plata es igual al doble de los que solo ob-
tuvieron medalla de bronce, elabora una
estrategia de resolución e indica cuántos
de los 30 estudiantes no obtuvieron meda-
lla si, además, el número de estudiantes que
ganaron medalla de plata es el doble de los
que obtuvieron medaila de oro.
Resolución:

Ask by Ray Fleming. in Peru
Mar 26,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

Todos los 30 estudiantes obtuvieron medallas, por lo que no hay estudiantes que no obtuvieron medalla.

Solución

Para resolver el problema, sigamos estos pasos:
  1. Definir las variables:
    • Sea : número de estudiantes que solo ganaron medalla de plata.
    • Sea : número de estudiantes que solo ganaron medalla de bronce.
    • Sea : número de estudiantes que solo ganaron medalla de oro.
    • Sea : número de estudiantes que ganaron medallas de oro y bronce.
    • Sea : número de estudiantes que ganaron medallas de oro y plata.
    • Sea : número de estudiantes que ganaron medallas de plata y bronce.
    • Sea : número de estudiantes que ganaron las tres medallas.
  2. Extraer la información del problema:
    • (3 estudiantes obtuvieron las tres medallas).
    • (5 estudiantes obtuvieron medallas de oro y bronce).
    • (1 estudiante obtuvo solo medalla de oro y plata).
    • (5 estudiantes obtuvieron solo medalla de bronce).
    • (3 estudiantes obtuvieron solo medalla de oro).
    • (el número de estudiantes que solo ganaron medalla de plata es igual al doble de los que solo obtuvieron medalla de bronce, por lo que ).
    • El número total de estudiantes es 30.
  3. Plantear la ecuación:
    La suma de todos los estudiantes que obtuvieron medallas es:
    Sustituyendo los valores conocidos:
  4. Resolver la ecuación:
    Simplificamos la ecuación:
    Por lo tanto:
  5. Calcular el número de estudiantes que no obtuvieron medalla:
    El número total de estudiantes que obtuvieron medallas es:
Por lo tanto, todos los estudiantes obtuvieron medallas y no hay estudiantes que no obtuvieron medalla.

Respondido por UpStudy AI y revisado por un tutor profesional

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Beyond the Answer

¡Vamos a desglosar el problema como si fuéramos detectives en una emocionante búsqueda para descubrir cuántos estudiantes no obtuvieron medallas!
  1. Contamos los estudiantes que recibieron medallas:
    • 3 estudiantes tienen oro, plata y bronce.
    • 5 estudiantes tienen oro y bronce.
    • 1 estudiante tiene solo oro y plata.
    • 5 estudiantes tienen solo bronce.
    • 3 estudiantes tienen solo oro.
    • Sea el número de estudiantes que solo ganaron plata. Sabemos que (porque el número de estudiantes que solo obtuvieron bronce es 5).
  2. Sumemos todos los estudiantes que obtuvieron medallas:
    • Total con oro, plata y bronce: .
  3. Calculamos los estudiantes que no obtuvieron medallas:
    • Si hay 30 estudiantes en total y 27 recibieron medallas, entonces .
Finalmente, encontramos que 3 estudiantes no obtuvieron medallas. ¡Caso cerrado! 🎉

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