Math, asked by uhmad, 6 months ago

A women sells to the first customer half her stock of apples and half an apple , to the second customer she sells half her remaining stock and half an apple , and so on to the third and to the fourth customer. She finds that she has now 15 apples left . How many apples did she have before she started selling?​

Answers

Answered by Anonymous
1

Answer:

\huge\underline\bold {Answer:}

Suppose she had x apples in the beginning.

Sold to the first customer

 \frac{x}{2}  +  \frac{1}{2}  =  \frac{x + 1}{2} \\

Remaining stock

 = x -  \frac{x + 1}{2}  =  \frac{2x - x - 1}{2}  \\  =  \frac{x - 1}{2}

Sold to the second customer

 =  \frac{1}{2}  \times  \frac{x - 1}{2}  +  \frac{1}{2}  \\  =  \frac{x - 1}{4}  +  \frac{1}{2}

 =  \frac{x - 1 + 2}{4}  =  \frac{x + 1}{4}

Remaining stock

 = ( \frac{x - 1}{2})  - ( \frac{x + 1}{4} ) \\  =  \frac{2x - 2 -  x - 1}{4}  \\  =   \frac{x - 3}{4}

Sold to the third customer

 =  \frac{1}{2}  \times  \frac{x - 3}{4}  +  \frac{1}{2}  \\  =  \frac{x - 3 + 4}{8}  \\  =  \frac{x + 1}{8}

Remaining stock

 = ( \frac{x - 3}{4} ) - ( \frac{x + 1}{8} ) \\  =  \frac{2x - 6 - x - 1}{8}  =  \frac{x - 7}{8}

Sold to the fourth customer

 =  \frac{1}{2}  \times  \frac{x - 7}{16}  +  \frac{1}{2}  \\  =  \frac{x - 7}{16}  +  \frac{1}{2}  \\  =  \frac{x - 7 + 8}{16}  \\  =  \frac{x + 1}{16}

Therefore,

x -  (  \frac{x + 1}{2}  +  \frac{x + 1}{4}  +  \frac{x + 1}{8}  +  \frac{x + 1}{16} ) \\  = 15

 =  > x - ( \frac{8x + 8 + 4x + 4 + 2x + 2 + x + 1}{16} ) \\  = 15

 =  > x - ( \frac{15x + 15}{16} ) = 15 \\  =  >  \frac{16 x - 15x - 15}{16}  \\  = 15 \\  =  >x  - 15 = 16 \times 15 = 240 \\  =  > x = 240 + 15 = 255.

Therefore, she had 225 apples before she started selling.

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