Mathematics

Question

Gina, Sam, and Robby all rented movies from the same video store. They each rented some dramas, comedies, and documentaries. Gina rented 11 movies total. Sam rented twice as many dramas, three times as many comedies, and twice as many as many documentaries as Gina. He rented 27 movies total. If Robby rented 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, how many movies of each type did Gina rent?

2 Answer

  • Solve using equations:

    Gina 11 = a+b+c
    Sam 27 = 2a+3b+2c
    Robby 19= a+2b+2c

    Gina *2 give 22=2a+2b+2c (subtract this from Sam to give)
    b=5

    the subtract Robby from Gina *2 to give a=3



    [Question 1]
    let d = number of dramas Gina rented, c = # of comedies, and t = # of documentaries:

    [equation a] d + c + t = 11
    [equation b] 2d + 3c + 2t = 27
    [equation c] d + 2c + 2t = 19

    if we subtract [a] from [c] we get:
    [equation d] c + t = 8

    if we subtract [c]*2 from [b] we get:
    [equation e] -c - 2t = -11 or
    [equation e] c + 2t = 11

    Now we can subtract [e] from [d] to solve for t:
    t = 3

    Now put in 3 for t in [d] or [e] to solve for c:
    c + 2(3) = 11
    c + 6 = 11
    c = 5

    So she rented 5 comedies and 3 documentaries which leaves 3 dramas (which is answer A)
  • Answer:

    The number of dramas movies Gina rented are 3 , number of comedies movies Gina rented are 5 and number of documentaries Gina rented are 3 .

    Step-by-step explanation:

    As given

    Gina, Sam, and Robby all rented movies from the same video store.

    They each rented some dramas, comedies, and documentaries.

    Gina rented 11 movies total.

    Let us assume that the number of dramas movies Gina rented be x .

    Let us assume that the number of comedies movies Gina rented be y .

    Let us assume that the number of documentaries movies Gina rented be z .

    Than the equation becomes

    x + y + z = 11

    As given

    Sam rented twice as many dramas, three times as many comedies, and twice as many as many documentaries as Gina.

    Sam rented 27 movies total.

    Number of dramas movies Sam rented = 2x

    Number of comedies movies Gina rented = 3y

    Number of documentaries movies Gina rented = 2z

    Than the equation becomes

    2x + 3y + 2z = 27

    As given

    Robby rented 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina .

    Number of dramas movies Robby rented = x

    Number of comedies movies Robby rented = 2y

    Number of documentaries movies Robby rented = 2z

    Than the equation becomes

    x + 2y + 2z = 19

    Thus the three equation in the form are

    x + y + z = 11

    2x + 3y + 2z = 27

    x + 2y + 2z = 19

    Multiply x + y + z = 11 by 2 and subtracted from 2x + 3y + 2z = 27 .

    2x - 2x + 3y - 2y + 2z - 2z = 27 - 22

    y = 5

    Subtracted x + 2y + 2z = 19 from 2x + 3y + 2z = 27 .

    2x - x + 3y - 2y + 2z -2z = 27 - 19

    x + y = 8

    Put y = 5 in the above equation

    x + 5 = 8

    x = 8-5

    x = 3

    Putting x = 3 , y = 5 in the equation x + y + z = 11 .

    3 + 5 + z = 11

    z = 11 - 8

    z = 3

    Therefore the number of dramas movies Gina rented are 3 , number of comedies movies Gina rented are 5 and number of documentaries Gina rented are 3 .



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