.
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.
ANSWER. 117 pennies, 60 dimes and 117-60 = 57 nickels.
CHECK. a) 117 + 60 + 57 = 234 coins. ! Correct !
b) 117 + 60*10 + 5*57 = 1002 cents. ! Precisely correct !
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 MAJOR LESSON for you from my solution.