Grandmother and grandfather

Grandmother baked cakes. Grandfather ate half, then quarter of the rest ate Peter and Paul ate half of rest. For parents left 6 cakes. How many cakes maked the grandmother?

Correct answer:

x =  32

Step-by-step explanation:

$$\begin{gathered} x-x\mathrm{/}2-1\mathrm{/}4\cdot x\mathrm{/}2-1\mathrm{/}2\cdot (x-x\mathrm{/}2-1\mathrm{/}4\cdot x\mathrm{/}2)=6 \\ x-x\mathrm{/}2-1\mathrm{/}8\cdot x-1\mathrm{/}2\cdot 3\mathrm{/}8\cdot x=6 \\ {\displaystyle \frac{3}{8}}\cdot x-{\displaystyle \frac{1}{2}}\cdot {\displaystyle \frac{3}{8}}\cdot x=6 \\ 3\mathrm{/}8\cdot x-3\mathrm{/}16\cdot x=6 \\ 3x=96 \\ x=32=32 \end{gathered}$$

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