Grandmother and grandfather

Grandmother baked cakes. Grandfather ate half, then a quarter of the rest ate Peter, and Paul ate half of the rest. There left six cakes for parents. How many cakes were made by the grandmother?

Correct answer:

x =  32

Step-by-step explanation:

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

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