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

Answer:

1. 36 rocks in total.

2. 15 purple rocks more than blue rocks

Step-by-step explanation:

1. Purple rocks are $\dfrac{2}{3}$ of all rocks, then the remainder is $1-\dfrac{2}{3}=\dfrac{1}{3}$ of all rocks.

2. Blue rocks are $\dfrac{3}{4}$ of the remainder, then blue rocks are

$\dfrac{3}{4}\cdot \dfrac{1}{3}=\dfrac{1}{4}$ of all rocks.

3. Silver rocks are the rest, that is

$\dfrac{1}{3}-\dfrac{1}{4}=\dfrac{4-3}{3\cdot 4}=\dfrac{1}{12}$ of all rocks.

4. It is known that the number of silver rocks is 3, then if x is the number of all rocks, $\dfrac{1}{12}$ of x is 3:

$\dfrac{1}{12}\cdot x=3,\\ \\x=3\cdot 12,\\ \\x=36.$

Hannah has 36 rocks in total. 3 of them are silver, $\dfrac{1}{4}\cdot 36=9$ are blue and $\dfrac{2}{3}\cdot 36=24$ are purple. Then she has $24-9=15$ more purple rocks than blue.