SOLUTION: A bank contains 36 nickels, dimes, and quarters. There are 4 more dimes than quarters and twice as many nickels as quarters. How many of each coin are in the bank? ***please write

Algebra ->  Equations -> SOLUTION: A bank contains 36 nickels, dimes, and quarters. There are 4 more dimes than quarters and twice as many nickels as quarters. How many of each coin are in the bank? ***please write      Log On


   

Question 997599: A bank contains 36 nickels, dimes, and quarters. There are 4 more dimes than quarters and twice as many nickels as quarters. How many of each coin are in the bank? ***please write the equation to this and solve for how many coins***
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = number of nickels
Let +d+ = number of dimes
Let +q+ = number of quarters
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(1) +n+%2B+d+%2B+q+=+36+
(2) +d+=+q+%2B+4+
(3) +n+=+2q+
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There are 3 unknowns and 3 equations,
so it is solvable
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Substitute (2) and (3) into (1)
(1) +2q+%2B+q+%2B+4+%2B+q+=+36+
(1) +4q+%2B+4+=+36+
(1) +4q+=+32+
(1) +q+=+8+
and
(2) +d+=+q+%2B+4+
(2) +d+=+8+%2B+4+
(2) +d+=+12+
and
(3) +n+=+2q+
(3) +n+=+2%2A8+
(3) +n+=+16+
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There are 16 nickels, 12 dimes, and 8 quarters
check:
(1) +n+%2B+d+%2B+q+=+36+
(1) +16+%2B+12+%2B+8+=+36+
(1) +36=+36+
OK