Question 1138285
.
<pre>
Let N be the number of nickels.

Then the number of dimes is 2N and the number of quarters is (21-N-2N) - (21-3N).


The "money" equation is


    5N + 10*(2N) + 25*(21-3N) = 275  cents.


Simplify and solve


    5N + 20N + 25*21 - 75N = 275


    -50N = 275 - 25*21


      N = {{{(275 - 25*21)/(-50)}}} = 5.


<U>ANSWER</U>.  5 nickel,  2*5 = 10 dimes  and the rest 21 - 5 - 10 = 6 coins are quarters.


<U>CHECK</U>.   5*5 + 10*10 + 6*25 = 275 cents.    ! Correct !
</pre>