A man buys 52 coconuts, but some are lost on his way home. If he evenly divides the amount of coconuts he has left among four people, 3 coconuts are left. If he divides the coconuts among three people, 2 remain. And if he divides the coconuts among five people, he's left with 2 coconuts. How many coconuts did he lose on his way home?
please help ;-;
Answers
Answer:
There are 5 coconuts which lost in the way.
Step-by-step explanation:
If A man buys 52 coconuts then according to conditions given in the question.
If some coconuts the lost by man in a way then for remaining coconuts there are following properties
If remaining coconuts are in such a way that the dividing by 4 give the remainder 3 then possibilities are following
7 , 11 , 15 , 19 , 23 , 27 , 31 , 35 , 39 , 43 , 47 , 51
If remaining coconuts are in such a way that the dividing by 3 give the remainder 2 then possibilities are following
5 , 8 , 11 , 14 , 17 , 20 , 23 , 26 , 29 , 32 , 35 , 38 , 41 , 44 , 47 , 50
If remaining coconuts are in such a way that the dividing by 5 give the remainder 2 then possibilities are following
7 , 12 , 17 , 22 , 27 , 32 , 37 , 42 , 47 , 52
As we see the common possibility is following
47
Thus
Remaining coconuts are 47 and
Lost = 52 - 47 = 5
There are 5 coconuts which lost in the way