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?
Hannah has 36 space rocks total. How many more purple rocks does Hannah have than blue rocks?

She has 15 more purple rocks than blue.

Step-by-step explanation:

purple= 2/3 of all rocks

blue= 3/4 of all rocks that aren't purple

silver= 3 (or 1/4 of all rocks that aren't purple)

if 3 (silver) is 1/4 of all rocks that aren't purple, blue (3/4) is 3x3=9

if purple is 2/3 of all rocks, blue and silver are 1/3 of all rocks

so 1/3 of all rocks would be 9+3=12

if 1/3=12, then 2/3 (purple)=24

At this point:

purple=24

blue=9

silver=3

purple (24) - blue (9) =15

She has 15 more purple rocks than she does blue.

I answered this question previously

the least common denominator is 40