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UkoKoshka [18]
3 years ago
11

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?
Mathematics
1 answer:
oksian1 [2.3K]3 years ago
6 0

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.


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