How many Eggs?
A woman took a certain number of eggs to the market and sold some of them.
The next day, through the industry of her hens, the number left over had been doubled, and she sold the same number as the previous day.
On the third day the new remainder was tripled, and she sold the same number as before.
On the fourth day the remainder was quadrupled, and her sales the same as before.
On the fifth day what had been left over were quintupled, yet she sold exactly the same as on all the previous occasions and so disposed of her entire stock.
What is the smallest positive number of eggs she could have taken to market the first day, and how many did she sell daily?
**Answer Format: Number of eggs on First day.Eggs Sold Daily
Example: If Number of Eggs = a and Eggs sold daily = b
Answer = a.b
The answer is 103.60.
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1 solution
She took 103 eggs to market on the first day and sold 60 eggs everyday.
Let's assume that she had N eggs on the first day and she sold X eggs everyday. Putting down the given information in the table as follow.
Days..........Eggs at the start of the day..........Eggs Sold...........Eggs Remaining
Day 1.......................N.....................................................X.................................N-X
Day 2....................2N-2X...............................................X.................................2N-3X
Day 3.....................6N-9X..............................................X.................................6N-10X
Day 4...................24N-40X...........................................X.................................24N-41X
Day 5..................120N-205X.......................................X................................120N-206X
It is given that she disposed of her entire stock on the fifth day. But from the table above, the number of eggs remaining are ( 120 N - 206 X ). Hence,
120N - 206X = 0
120N = 206X
60N = 103X
The smallest value of N and X must be 103 and 60 respectively. Hence, she took 103 eggs to market on the first day and sold 60 eggs everyday.