Answer:
1. 36 rocks in total.
2. 15 purple rocks more than blue rocks
Step-by-step explanation:
1. Purple rocks are [tex]\dfrac{2}{3}[/tex] of all rocks, then the remainder is [tex]1-\dfrac{2}{3}=\dfrac{1}{3}[/tex] of all rocks.
2. Blue rocks are [tex]\dfrac{3}{4}[/tex] of the remainder, then blue rocks are
[tex]\dfrac{3}{4}\cdot \dfrac{1}{3}=\dfrac{1}{4}[/tex] of all rocks.
3. Silver rocks are the rest, that is
[tex]\dfrac{1}{3}-\dfrac{1}{4}=\dfrac{4-3}{3\cdot 4}=\dfrac{1}{12}[/tex] of all rocks.
4. It is known that the number of silver rocks is 3, then if x is the number of all rocks, [tex]\dfrac{1}{12}[/tex] of x is 3:
[tex]\dfrac{1}{12}\cdot x=3,\\ \\x=3\cdot 12,\\ \\x=36.[/tex]
Hannah has 36 rocks in total. 3 of them are silver, [tex]\dfrac{1}{4}\cdot 36=9[/tex] are blue and [tex]\dfrac{2}{3}\cdot 36=24[/tex] are purple. Then she has [tex]24-9=15[/tex] more purple rocks than blue.
