SOLUTION: In the cash drawer at a bank, the ratio of the number of $1 bills to the number of $5 bills is 5 to 4, and the ratio of $10 bills to $20 bills is 2 to 1. These bills represent the

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Question 586013: In the cash drawer at a bank, the ratio of the number of $1 bills to the number of $5 bills is 5 to 4, and the ratio of $10 bills to $20 bills is 2 to 1. These bills represent the total amount of money in the drawer: $6795. How many $1 bills are in the drawer?
I know how to do basic ratio problems, but being that this one involves money, it just confuses me... Please help! I would /really/ appreciate it.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The way I do it is:
Let a = number of $1 bills
Let b = number of $5 bills
Let c = number of $10 bills
Let d = number of $20 bills
--------------------------
given:
(1) +a%2Fb+=+5%2F4+
(2) +c%2Fd+=+2%2F1+
(3) +1%2Aa+%2B+5%2Ab+%2B+10%2Ac+%2B+20%2Ad+=+6795+
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This is 4 unknowns and only 3 equations,
so it isn't completely solvable, but the
information can still be there
-----------------------
(1) +4a+=+5b+
(1) +b+=+%285%2F4%29%2Aa+
and
(2) +c+=+2d+
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The possible combinations of $1s and $5s is:
5 $1s
4 $5s
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10 $1s
8 $5s
-----
15 $1s = $15
12 $5s = $60
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Whatever combination I choose, the remainder of the money
must be divisible by $40 ( 1 $20 and 2 $10s )
+6795+-+75+=+6720+
+6720%2F40+=+168+
this seems to work
168 $20s = $3360
336 $10s = $3360
12 $5s = $60
15 $1s = $15
------------
sum = $6795
I don't know if another combination will work.
This one seems to.