Question 1200567
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A collection of nickels, dimes, and quarters is retrieved from a vending machine. 
There are three times as many nickels as dimes, and there are ten more quarters than dimes. 
If the total value of the coins is $40.00 then find the number of each type of coin.
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            It may seem fantastic,  but the problem can be 

            solved mentally,  without using equations.



<pre>
Take 10 quarters aside, for a minute.


Then the updated collection has three times as many nickels as dimes, 
and the same number of quarters as dimes and it is worth 

    40.00 - 10*0.25 = 40 - 2.50 = 37.50 dollars.


Now group the coins in the sets, combining 1 dime, three nickels and 1 quarter in each set.
According to the problem, it CAN BE DONE.


Each set is worth  10 + 3*5 + 25 = 50 cents; so, the number of sets is  {{{37.50/0.5}}} = 75.


From this, we conclude that the original collection has 
75 dimes, 3*75 = 225 nickels and 75+10 = 85 quarters.      <U>ANSWER</U>
</pre>

Solved.


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Good problem for a school &nbsp;Math circle to give it to advanced students
and ask them to solve it &nbsp;MENTALLY, &nbsp;without using equations.



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If a Math teacher wants to bring up students with vivid mind, he (or she)
should give them such assignments from time to time.