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Jose was playing a game with marbles.In the first round ,he lost 1/4 of his marbles.In the Second round,he lost 1/3 of his remaining marbles.In the third round,he lost 1/2 of his remaining marbles.He gave 1 marbles to his friend shavana.He had 1 marble left.
How many marbles did jose start with?

  • math -

    x= total marbles
    x-(1/4)x what he had after 1st round
    (x-(1/4)x)-1/3(x-(1/4)x) what he had left after 2nd
    (x-(1/4)x)-1/3(x-(1/4)x)-1/2((x-(1/4)x)-1/3(x-(1/4)x)) what he had left after 3rd round which equals 2 (the one he gave to Shavana and the one he kept)
    (x-(1/4)x)-1/3(x-(1/4)x)-1/2((x-(1/4)x)-1/3(x-(1/4)x))=2
    solving:
    x-(1/4)x-(1/3)x+(1/12)x-(1/2)x+(1/8)x+(1/6)x-(1/24)x=2
    Factoring out x and making like fractions
    x(1-6/24-8/24+2/24-12/24+3/24+4/24-1/24)=2
    x(24/24-6/24-8/24+2/24-12/24+3/24+4/24-1/24)=2
    x(33/24-27/24)=2
    (1/4)x=2
    x=8
    SO HE START WITH 8
    he lost 2 the first round leaving him with 6
    he lost (1/3) of 6 the 2nd round leaving him with 4
    and he lost (1/2) the 3rd round leaving him with 2

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