7th grade Math

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Two bags contain the same number of marbles. In one bag, the ratio of black marbles to white marbles is 4:3. In the other bag, the ratio is 3:2. Which bag contains more black marbles?

Thanks!

  • 7th grade Math -

    Assume that there are 100 marbles in each bag.

    Firstly divide 100 by 7 (ratio 4:3) 14.28.

    Multiply 14.28 by 4 = 57.12 *57 marbles
    Mulitply 14.28 by 3 = 42.84 *53 marbles

    Secondly do the same for ratio 3:2

    Divide 100 by 5 = 20

    Multiply 20 by 3 = 60 marbles
    Multiply 20 by 2 = 40 marbles.

    Therefore the second bag contains more black marbles.

  • 7th grade Math -

    Hi Kelly,

    For this one.

    Multiply 14.28 by 3 = 42.84 *53 marbles

    Do you mean to say *43 marbles? rounded up from 42.84?

    Thanks for your help.

  • 7th grade Math -

    Change the ratio so that the second number is the same
    4:3 = 8:6 , first # stands for black, 2nd # stands for white

    3:2 = 9:6

    clearly the 2nd has more black marbles

  • 7th grade Math -

    Hi Reiny,

    Before posting this question, I thought the same way by putting the same amount of white marbles but if you add the total amount of marbles for both bags and that wouldn't be equal since the question mentioned "Two bags contain the same number of marbles".

    4:3 = 8:6 (14 marbles)
    3:2 = 9:6 (15 marbles)

    Let me know if I'm wrong.

    Thanks!

  • 7th grade Math -

    you say:
    4:3 = 8:6 (14 marbles)
    why not keep going...
    14 marbles or 28 , or 42 , 56 , ....

    3:2 = 9:6 (15 marbles)
    why not keep going
    15 marbles or 30, 45 , ...

    when are they the same ?
    What number divides by both 15 and 14 ?
    210

    So suppose each bag has 210 marbles
    first bag: 4:3 ratio -- > 120 black to 90 white
    2nd bag: 9:6 --> 126 black to 84 white

  • 7th grade Math -

    Thank you again.

  • 7th grade Math -

    Sorry Eric, yes I did mean 43 (typo sorry)

  • 7th grade Math -

    thanks!!!!!!!!!

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