A group of three friends ate dinner at a restaurent. when they settled the check,peter paid 4/5 as much as?

A group of three friends ate dinner at a restaurant. when they settled the check,peter paid 4/5 as much as john paid,and john paid 1/3 as much as Ralph paid. what fraction of the check did john pay.

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  • David
    Lv 7
    9 years ago
    Favorite Answer

    P + J + R = 1

    P = (4/5)J

    P = 4J / 5

    J = (1/3)R

    J = R/3

    3J = R

    (4J / 5) + J + 3J = 1

    (4J / 5) + 4J = 1

    (4J + 20J) / 5 = 1

    24J = 5

    J = 5/24

    P = 1/6

    R = 15/24 = 5/8

  • 9 years ago

    lets assume that ralph paid X $

    then John paid 1/3*X

    and Peter paid 4/5*1/3*X= (4/15)*X

    Now for simplicity sake lets assume their bill was 100$

    therefore the sum paid by the 3 friends should equal 1

    therefore X + ((1/3)*X)+ ((4/15)*X) = 1

    thus, X(1+1/3+4/15)=1

    then, X(24/15)=1

    therefore X = 15/24

    Now john paid 1/3* X

    i.e. (1/3)*(15/24)

    = 5/24

    John paid 5/24th of the bill

  • Pranil
    Lv 7
    9 years ago

    peter = 4/5 john

    john = 1/3 Ralph

    Ralph = 3 john

    peter + john + Ralph = 1

    4/5 john + john + 3 john = 1

    4/5 john + 4 john = 1

    24/5 john = 1

    john = 5/24

    ----

  • None
    Lv 7
    9 years ago

    P = (4/5)J = (4/15) R

    J = (1/3)R

    P + J + R = (4/15)R + (1/3)R + R = (24/15)R

    J = (1/3)R/(24/15)R = 15/72 = 5/24 of the total

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