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Jack and Jill got an equal number of marbles from their grandpa's collection. Jill gave 50 marbles to Jack because she saw that he was more interested in marbles than she was. Now Jack has 5 times as many marbles as Jill. How many total marbles did grandpa give away and how many did they each get?

  • math -

    This is a logic problem. I will write out the steps below.

    Ja= Jack
    Ji= Jill

    Jill gives 50 to Jack, so she has 50 less and he has 50 more.

    And, this quantity of 50 more is equal to 5 times Jill's amount.

    So, now Jill has Ji-50 and Jack has Ja + 50

    So, now just think how to set this up algebraically: If they both had 100 to start with, and Jill gives away 50, she has 50 now, and Jack has 150. So, the difference between the two will always be 100, no matter what number you choose for the beginning value. So, Jill will have 100 less marbles than Jack now.

    Ji= Ja- 100

    Now we develop a new relationship:
    Ja= 5 Ji
    Ja= 5 ( Ja - 100)
    Ja= 5Ja-500
    Ja + 500= 5Ja
    4Ja= 500
    Ja= 125

    Now solve for Ji using Ja= 5 Ji
    125= 5 Ji
    J= 25

    Now since Jill gave him 50 and he took 50, you subtract 50 from his pile, and add 50 to hers.

    So, Jill had 75 to begin with and Jack had 75 to begin with.

    Check backwards:

    75-50= 25= Ji now
    75 + 50= 125= Ja now

    Is this statement true: Ja= 5 Ji?
    125= 5 * 25
    125= 125
    Yes! It is. So, this is your answer!

    Hope this helps!

  • math -

    This is a question to the answer above
    Got it. I was confused with the question because what if they did NOT start with the same amount but did receive same amount from grandpa? Is that a different problem or cannot be done?

  • math -

    Yoyoma, can you please answer the question on what if Jack & Jill did NOT start with equal amount of marbles?

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