Question 1205719
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Katie has a collection of nickels, dimes and quarters with a total value of $6.80. 
There are 5 more dimes than nickels and 6 more quarters than nickels, how many of each coin does she have?
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Let x be the number of nickels;

then the number of dimes is (x+5) and the number of quarters is (x+6).


Write the total money equation in cents

    5x + 10*(x+5) + 25*(x+6) = 680 cents.


Simplify and find x

    5x + 10x + 50 + 25x + 150 = 680

    5x + 10x + 25x = 680 - 50 - 150

         40x       =      480

           x       =      480/40 = 12.


<U>ANSWER</U>.  There are 12 nickels,  12+5 = 17 dimes  and  12+6 = 18 quarters.


<U>CHECK</U>.   12*5 + 17*10 + 18*25 = 680 cents, total.    ! correct !
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Solved.