Hannah 2

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?

Correct answer:

n =  36

Step-by-step explanation:

$$\begin{gathered} a=\frac{2}{3}\doteq 0.6667 \\ r=1-a=1-\frac{2}{3}=\frac{1\cdot 3}{3}-\frac{2}{3}=\frac{3}{3}-\frac{2}{3}=\frac{3-2}{3}=\frac{1}{3}\doteq 0.3333 \\ b=\frac{3}{4}\cdot r=\frac{3}{4}\cdot \frac{1}{3}=\frac{3\cdot 1}{4\cdot 3}=\frac{3}{12}=\frac{1}{4}=0.25 \\ c=1-a-b=1-\frac{2}{3}-\frac{1}{4}=\frac{1}{12}\doteq 0.0833 \\ C=3 \\ C=c\cdot n \\ n=C/c=3/\frac{1}{12}=3:\frac{1}{12}=3\cdot \frac{12}{1}=\frac{3\cdot 12}{1}=\frac{36}{1}=36 \\ \text{ Verifying Solution: } \\ A=a\cdot n=0.6667\cdot 36=24 \\ B=b\cdot n=0.25\cdot 36=9 \end{gathered}$$

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