math
posted by Adi on .
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?

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(16/248/24+2/2412/24+3/24+4/241/24)=2
x(24/246/248/24+2/2412/24+3/24+4/241/24)=2
x(33/2427/24)=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