Question

An egg vendor calls on his first customer and sells half his eggs and half an egg. To the second customer, he sells half of what he has left with and half an egg, and to the third customer, he sells half of what he was then left with and half an egg. However, he did not break any egg. If in the end, the vendor was left with three eggs did he have initially?

• A. $26$
• B. $31$
• C. $39$
• D. None of these

Answer 1

The correct option is B $31$

Let the vendor have x eggs initially,

eggs sold to his first customer $=\frac{x}{2}+0.5$,

eggs left $=x-\frac{x}{2}+0.5=\frac{x}{2}-0.5$,

eggs sold to his second customer$=\frac{\frac{x}{2}-0.5}{2}+0.5,eggsleft=\frac{x}{2}-0.5-\frac{x-1}{4}-0.5=\frac{x+1}{4}-1,$

eggs sold to his third customer$=\frac{\frac{x+1}{4}-1}{2}+0.5,eggsleft=\frac{x+1}{4}-1-\frac{x-3}{8}-0.5=\frac{x+5}{8}-1.5,\frac{x+5}{8}-1.5=3,⟹x=31$\\