Question

PLEASE HELP ASAP! 15 POINTS! 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

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Explanation:

Answer 2

1. 36 rocks in total.

2. 15 purple rocks more than blue rocks

Explanation:

1. Purple rocks are
`(2)/(3)` of all rocks, then the remainder is
`1-(2)/(3)=(1)/(3)` of all rocks.

2. Blue rocks are
`(3)/(4)` of the remainder, then blue rocks are

`(3)/(4)\cdot (1)/(3)=(1)/(4)` of all rocks.

3. Silver rocks are the rest, that is

`(1)/(3)-(1)/(4)=(4-3)/(3\cdot 4)=(1)/(12)` of all rocks.

4. It is known that the number of silver rocks is 3, then if x is the number of all rocks,
`(1)/(12)` of x is 3:

`(1)/(12)\cdot x=3,\\ \\x=3\cdot 12,\\ \\x=36.`

Hannah has 36 rocks in total. 3 of them are silver,
`(1)/(4)\cdot 36=9` are blue and
`(2)/(3)\cdot 36=24` are purple. Then she has
`24-9=15` more purple rocks than blue.