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(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
I have no idea! SORRY
To solve this problem, let's work backwards. We know that Jose had 1 marble left after all the rounds and giving one to his friend Shavana.
Step 1: After giving 1 marble to Shavana, Jose had 2 marbles left.
Step 2: In the third round, Jose lost half of his remaining marbles. Since he had 2 marbles left after the second round, we can calculate his marbles before the third round by undoing the loss.
To find Jose's marbles before the third round, we can calculate:
2 marbles * 2 = 4 marbles.
Step 3: Before the second round, Jose had 4 marbles.
In the second round, Jose lost one-third of his remaining marbles. So, to find Jose's marbles before the second round, we can calculate:
4 marbles * 3 = 12 marbles.
Step 4: Before the first round, Jose had 12 marbles.
In the first round, Jose lost one-fourth of his marbles. So, to find Jose's original number of marbles, we can calculate:
12 marbles * 4 = 48 marbles.
Therefore, Jose started with 48 marbles.