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1 November, 21:48

Allen has four times as many cards as Bob, and Jane has twice as many cards as Allen. Together, Allen and Jane have 468 cards. How many cards do Allen, Jane, and Bob each have?

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  1. 1 November, 22:01
    0
    156

    312 and

    39

    Step-by-step explanation:

    Let Allen be A, Jane be J and Bob be B

    Allen has 4 times as Bob

    So

    A = 4B

    Jane has twice as Allen

    So

    J = 2A

    Together, Allen and Jane has 468 cards

    A + J = 468

    Substitute 2A for J in the third equation.

    We have

    A + J = 468

    A + 2A = 468

    3A = 468

    Divide both sides by 3

    3A/3 = 468/3

    A = 156

    Recall

    A = 4B

    Therefore

    156 = 4B

    Divide both sides by 4

    156/4 = 4B/4

    39 = B

    B = 39

    Also,

    J = 2A

    J = 2 x 156

    J = 312

    Allen has 156 cards

    Jane has 312 cards and

    Bob has 39 cards
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