Question 743784
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Michael's bank contains only nickels, dimes, and quarters. There are 50 coins is all, value at $4.15. 
The number of nickels is 10 short of being three times the sum of the number of dimes and quarters together. 
How many dimes are in the bank?
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Let' solve it mentally.


Let's add 10 short nickels mentally. We will get 50+10 = 60 coins, with the number of nickels being three times 
of the sum of the number of dimes and quarters together.


It means that four times the number of dimes and quarters is 60/4 = 15 in the original collection,
with the number of nickels 3*15 - 10 = 35 in the original collection.


So, the original collection is 35 nickels plus 15 dimes and quarters (dimes and quarters are counted together).


Hence, 15 dimes and quarters in the original collection are worth 415 - 35*5 = 240 cents.


Had all 15 coins be dimes, it would be 150 cents, but we actually have 240 cents, or 90 cents more.


Hence, some dimes should be replaced by quarters.


Each such replacement increases the value of dimes and quarters by 15 cents, and the number of such replacements
should be, therefore, 90/15 = 6.


Thus, the original collection has 35 nickels, 6 quarters and 50 - 35 - 6 = 9 dimes.


<U>CHECK</U>.  Total coins = 35 + 6 + 9 = 50.

        Total money = 35*5 + 6*25 + 9*10 = 415 cents, or $4.15.

        The number of nickels is 3*(6+9) -10 = 3*15 - 10 = 45 - 10 = 35.

        Everything is correct.


<U>ANSWER</U>.  35 nickels, 9 dimes and 6 quarters.
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Solved.