Mark give 20% of his marbles to john and three eighths of the remainder to harry. if he had 40 remain, how many marbles he had a first?
0.2 m to mark, 0.9 m left
3/8 of 0.8 m to Harry, 5/8 of 0.8 m left
so
5/8 * 8/10 * m = 40
1/2 * m = 40
m = 2 * 40
typo, 0.8 left not 0.9
Mark has X marbles.
x-0.2x = 0.8x remains.
0.8x-3/8*0.8x = 0.8x-0.3x = 0.5x remainder.
0.5x = 40.
X =
so that means x equals 40 divided by 0.5 and that would be the answer.
To find out how many marbles Mark had at first, we can work backwards from the information given.
Let's assume that the number of marbles Mark had initially is M.
According to the question, Mark gives 20% of his marbles to John. Therefore, the amount of marbles Mark gives to John is 20% of M, which can be written as 0.2M.
After giving the marbles to John, the remaining number of marbles Mark has is M - 0.2M, which simplifies to 0.8M.
Now, three eighths of the remainder (0.8M) is given to Harry. Therefore, the amount of marbles Mark gives to Harry is (3/8) * 0.8M, which can be written as 0.3M.
After giving the marbles to Harry, the remaining number of marbles is 0.8M - 0.3M, which simplifies to 0.5M.
According to the question, this remaining number of marbles is given as 40. So we can write:
0.5M = 40
To find the value of M, we divide both sides of the equation by 0.5:
M = 40 / 0.5
M = 80
Therefore, Mark had 80 marbles at first.