Question

De Sean is Sorting his rock collection.$\frac{2}{3}$ of the rocks are metamorphic, and $\frac{3}{4}$ of the remainder are igneous rocks.

If the $3$ rocks left over are sedimentary, how many rocks does De Sean have?

Answer 1

Explanation For correct answer:

Let total rocks be $x$

Given,$\frac{2}{3}x$ are metamorphic then remaining are,

$x-\frac{2}{3}x$

then,$\frac{3}{4}$ remaining are igneous,

igneous

$$\begin{gathered} =\frac{3}{4}(x-\frac{2}{3}x) \\ =\frac{x}{4} \end{gathered}$$

Sedimentary $=3$left,

Total,

$$\begin{gathered} \Rightarrow x=\frac{2}{3}x+\frac{x}{4}+3 \\ \Rightarrow x=\frac{11}{12}x+3 \\ \Rightarrow x=12\times 3 \\ =36 \end{gathered}$$

Therefore, Desean has 36 rocks