Hannah finds purple blue and silver space rocks while exploring. 2 3 of the rocks are purple and 3 4 of the remainder are blue. If there are 3 silver rocks how many space rocks does Hannah have?

Let the total number of rocks be ( x ). If ( \frac{2}{3} ) of the rocks are purple, then the number of purple rocks is ( \frac{2}{3}x ). The remainder is ( x - \frac{2}{3}x = \frac{1}{3}x ), and ( \frac{3}{4} ) of these are blue, which gives ( \frac{3}{4} \times \frac{1}{3}x = \frac{1}{4}x ) as blue rocks. Adding the 3 silver rocks, we have:

[ \frac{2}{3}x + \frac{1}{4}x + 3 = x ]

Multiplying through by 12 to eliminate fractions gives ( 8x + 3x + 36 = 12x ), simplifying to ( 36 = x ). Therefore, Hannah has a total of 36 space rocks.