Question

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?

Answer 1

She has 15 more purple rocks than blue.

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.