SOLUTION: there is a piggy bank full of nickels, dimes and quarters. there are a total of 552 coins. the total value of these coins $76.65. The number of quarters is 43 more then the number

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Question 334059: there is a piggy bank full of nickels, dimes and quarters. there are a total of 552 coins. the total value of these coins $76.65. The number of quarters is 43 more then the number of nickels. I want to know how many coins there are of each type.
(i need to see the work please)
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
nickels,let the number be x
quarters is 43 more then the number of nickels.
quarters.= x+43
dimes = 552-(x+x+43)=552-(2x+43)
total of 552 coins.
the total value of these coins $76.65. = 7665 cents
..
Value equation
5x+25(x+43)+10[552-(2x+43)]=7665
..
5x+25x+1075+10[552-2x-43]=7665
30x+1075+5520-20x-430=7665
10x=7665-5520-1075+430
10x=1500
x= 150 the number of nickels
quarters = x+43= 193 quarters
dimes = 552-(2*150+43)=209
....
CHECK = 150+193+209=552
(5*150)+25(150+43)+10*(552-343))=7665