Question 961723
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A vending machine has $6.30 in it. There are 52 coins total and the machine only accepts nickels, 
dimes, and quarters. There are five more dimes than nickels. How many of each coin are in the machine ?
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            It is a typical problem to be solved using only one single unknown and only one single equation.



<pre>    
Let x be the number of nickels.

Then the number of dimes is (x+5), according to the condition.

The quarters are the rest coins, and their number is  (52-x-(x+5)) = (47-2x).


Having it, you write the total money equation


    5x + 10(x+5) + 25*(47-2x) = 630   cents.


Simplify and solve


    5x + 10x + 50 + 25*47 - 50x = 630

         -35x                   = 630 - 50 - 25*47 = -595

            x                                      = {{{(-595)/(-35)}}} = 17.


<U>ANSWER</U>.  17 nickels, 22 dimes and the rest 52 - 17-22 = 13  coins are quaters.


<U>CHECK</U>.  17*5 + 22*10 + 13*25 = 630 cents, in total.    ! Correct !
</pre>

Solved.



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It is how this problem is intended and is expected to be solved.



Only the persons UNFAMILIAR with a standard basic mathematical education principles, 


like &nbsp;@josgarithmetic or &nbsp;@Penguin, &nbsp;may think differently . . .