Candy

You stop at hasty to buy candy. You give half of the bag to one friend. Then give a quarter to another friend. Later two more friends come, and you give each of them a third of what is in the bag. How many candies did you start with?

Correct answer:

x =  0

Step-by-step explanation:

$$\begin{gathered} a=\frac{1}{2}=0.5 \\ A=1-a=1-\frac{1}{2}=\frac{1\cdot 2}{2}-\frac{1}{2}=\frac{2}{2}-\frac{1}{2}=\frac{2-1}{2}=\frac{1}{2}=0.5 \\ b=A/4=\frac{1}{2}/4=\frac{1}{2\cdot 4}=\frac{1}{8}=0.125 \\ B=A-b=\frac{1}{2}-\frac{1}{8}=\frac{4}{8}-\frac{1}{8}=\frac{4-1}{8}=\frac{3}{8}=0.375 \\ c=2\cdot B/3=2\cdot \frac{3}{8}/3=\frac{1}{4}=0.25 \\ x=C=B-c=\frac{3}{8}-\frac{1}{4}=\frac{3}{8}-\frac{2}{8}=\frac{3-2}{8}=\frac{1}{8}=0.125=0 \end{gathered}$$

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