Maths

A bag contains marbles of three different colours red, blue , yellow. 2/5 of the marbles are red. The ratio of the number of blue marbles to the number of yellow marbles is 5:7. What fraction of the marbles in the bag is blue? There are 54 more red marbles than blue marbles. How many marbles are there in the bag?

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  1. let the total be x
    (2/5)x = r , also b+54 = (2/5)x
    b = 2x/5 - 54 = (2x - 270)/5

    b : y = 5 : 7
    5y = 7b
    y = (7/5)b
    y = 7(2x-270)/25

    so 2x/5 + (2x-270)/5 + 7(2x-270)/25 = x
    times 25
    10x + 10x - 1350 + 14x - 1890 = 25x
    -9x = -3240
    x = 360

    we have 510 marbles

    check:
    red = (2/5)(360) = 144
    b = (720-270)/5 = 90
    y = (7/5)(90) = 126

    144+90+126 = 360 , check!
    blue : yellow = 90 : 126 = 5 : 7 , check
    area there 54 more reds than blues?
    144-90 = 54, check!

    there are 510 marbles

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  2. I obviously got x = 360

    So there are 360 marbles,

    I have no idea where I got the 510 from, and then I copied it again at the end.
    Time for my third cup of coffee.

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