Question 1149610
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From the condition, the number of pennies is half of 234, i.e.  234/2 = 117.


Thus the number of nickels PLUS dimes is 117, too, and these two type of coins are worth  1002 - 117 = 885 cents.


Now, if the number of dimes is x, then the number of nickels is  (117-x),

and the money equation is


    5*(117-x) + 10x = 885  cents,    or

    
     117-x + 2x = 885/5 = 177,

     x = 177 - 117 = 60.


<U>ANSWER</U>.  117 pennies, 60 dimes  and  117-60 = 57 nickels.


<U>CHECK</U>.   a)  117 + 60 + 57 = 234  coins.           ! Correct !

         b)  117 + 60*10 + 5*57 = 1002  cents.     ! Precisely correct !
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Solved.


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This problem seems to be on 3 equations in 3 unknowns.


But using the logic and a technique, presented in my post, it admits reducing to one single equation in one unknown,

which can be easily solved.


It is the &nbsp;<U>MAJOR &nbsp;LESSON</U> &nbsp;for you from my solution.