Question 203989
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Jon throws all his nickels and dimes in a jar at home each day. 
He counted all his coins one day and found that he had collected $42.35. 
If there were five times as many nickels as dimes how many of each coin does he have?
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        This is a typical example of problems on coins 
        that can be solved  MENTALLY  in couple of lines without using any equations.



<pre>
According to the problem, we can group all coins in sets each containing 5 nickels and 1 dime.


Each such a group is worth  5*5 + 10 = 25 + 10 = 35 cents.


Now we can determine the number of such groups of coins.  It is

    {{{4235/35}}} = {{{4200/35}}} + {{{35/35}}} = {{{(2*4200)/(2*35)}}} + 1 = {{{8400/70}}} + 1 = {{{840/7}}} + 1 = 120 + 1 = 121.


So, there are 121 dimes and 5*121 = 605 nickels.     <U>ANSWER</U>
</pre>

Solved mentally in 5 lines.


It is nice and instructive, isn't ?