Question 1149610: Emma paid the $10.02 bill for her lunch with 234 coins consisting of pennies, nickels and dimes. If the number of nickels plus dimes was equal to the number of pennis then how many coins of each type did she use?
She used ___pennis, ____, nickels, _____,dimes
Answer by ikleyn(52794)   (Show Source):
You can put this solution on YOUR website! .
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.
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