Harry has 0.6 of his marbles to his younger bro and 0.5 of the remainder to his cousin. Harry has 36 marbles left. How many marbles did harry have at first ?
after giving .6x to his brother, he has .4x left
he gives half of those to the cousin.
So he has .2x left
.2x = 36
x = 180
Well, it seems like Harry is quite generous with his marbles! Let's put our mathematical hats on and solve this puzzle.
If Harry gave away 0.6 of his marbles to his younger brother, then he would have 0.4 of his marbles remaining.
Now, if Harry gave away 0.5 of the remaining marbles to his cousin, it means he would have 0.5 multiplied by 0.4 of his original marbles left.
So, to find the number of marbles Harry had at first, we need to solve the equation:
0.5 * 0.4 * x = 36
Now, let me get my trusty calculator... *beep boop beep*
It seems like Harry had approximately 90 marbles at the beginning! Boy, that's a lot of marbles to go around!
Let's assume Harry initially had x marbles.
Harry gives 0.6x marbles to his younger brother, so he has 0.4x marbles left.
He then gives 0.5(0.4x) = 0.2x marbles to his cousin, leaving him with 0.4x - 0.2x = 0.2x marbles.
Given that Harry has 36 marbles left, we have the equation 0.2x = 36.
To solve for x, we divide both sides of the equation by 0.2: x = 36 / 0.2 = 180.
Therefore, Harry initially had 180 marbles.
To solve this problem, we can work backwards by undoing the actions that Harry took with his marbles.
Let's start with the fact that Harry has 36 marbles left. We know that at one point, Harry gave 0.6 of his marbles to his younger brother. This means that his younger brother now has 0.6 * 36 = 21.6 marbles.
Next, we know that Harry gave 0.5 of the remainder to his cousin. So, we need to find out what the remainder was after giving marbles to his younger brother. We can do this by dividing the number of marbles his younger brother has by 0.6. Therefore, the remainder is (21.6 / 0.6) = 36 marbles.
Now, we have found the remainder after giving marbles to his cousin. Let's find the number of marbles Harry had before giving any away. We can do this by dividing the remainder by 0.5. So, the number of marbles Harry had at first is (36 / 0.5) = 72 marbles.
Therefore, Harry had 72 marbles at first.