SOLUTION: a bank has nickels, dimes, and quarters. There are fewer dimes than nickels and three times as many quarters as dimes. If the total amount in the bank is $7.45, how many of each co

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Question 1166493: a bank has nickels, dimes, and quarters. There are fewer dimes than nickels and three times as many quarters as dimes. If the total amount in the bank is $7.45, how many of each coin is there
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
n, d, q

system%28d%3Cn%2Cand%2Cq%2Fd=3%29

That also shows q=3d.

5n%2B10d%2B25q=745
n%2B2d%2B5q=149
substituting for q,
n%2B2d%2B15d=149
n%2B17d=149


Not yet finished, you want whole numbers n and d so that
system%28n%3Ed%2Cand%2Cn%2B17d=149%29.
.
.
(just a quick thought - what if d were 8? Whole n greater than 8 ?)

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the number of dimes.

Then the number of quarters is 3x.


Let y be the number of nickels.


Then we could write the total money equation in the form


    5y + 10x + 25*(3x) = 745  cents,  or

    5y + 85x           = 745,


which is the same as

    y + 17x = 149.

We know that x < y.


Make a table


    x, dimes    y, nickels = 149 - 17x


      1		132
      2		115
      3		98
      4		81
      5		64
      6		47
      7		30
      8		13


This table is the list of possible answers.


Remember that the number of possible quarters is 3x.

Solved.