Harrh gives 0.6 of his marbles to his younger brother and 0.5 of the remainder to his cousin. Harry has 36 marbles left. How many marbles did Harry have at first?
starting number ---- x
after giving to younger brother, number left = .4x
gives away half of that, so left with .2x
.2x = 36
x = 36/.2 = 180
Let's assume Harry initially had 'x' marbles.
According to the given information, Harry gives 0.6 of his marbles to his younger brother, which is equivalent to 0.6x marbles.
After giving 0.6x marbles to his younger brother, Harry is left with (x - 0.6x) = 0.4x marbles.
Next, Harry gives 0.5 of the remainder to his cousin, which is equivalent to 0.5 * 0.4x = 0.2x marbles.
After giving 0.2x marbles to his cousin, Harry is left with (0.4x - 0.2x) = 0.2x marbles.
According to the given information, Harry has 36 marbles left, so we can set up the equation:
0.2x = 36
Dividing both sides of the equation by 0.2, we get:
x = 36 / 0.2
Simplifying the equation, we find:
x = 180
Hence, Harry initially had 180 marbles.