SOLUTION: Elisa has $151 in her wallet, consisting of $20, $5, and $1 bills. The number of $20 bills is three less than the number of $5 bills. If she has 24 bills in her wallet, how many of

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Elisa has $151 in her wallet, consisting of $20, $5, and $1 bills. The number of $20 bills is three less than the number of $5 bills. If she has 24 bills in her wallet, how many of      Log On

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Question 190775: Elisa has $151 in her wallet, consisting of $20, $5, and $1 bills. The number of $20 bills is three less than the number of $5 bills. If she has 24 bills in her wallet, how many of each denomination does she have?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a= the number of $1 bills
Let b= the number of $5 bills
Let c= the number of $20 bills
given:
(1) c+=+b+-+3
(2) a+%2B+b+%2B+c+=+24
(3) 1a+%2B+5b+%2B+20c+=+151
----------------------------
Subtract (2) from (3)
4b+%2B+19c+=+127
Substitute c in (1)
4b+%2B+19%2A%28b+-+3%29+=+127
4b+%2B+19b+-+57+=+127
23b+=+184
b+=+8
and, from (1)
c+=+8+-+3
c+=+5
And using (2)
a+%2B+b+%2B+c+=+24
a+%2B+8+%2B+5+=+24
a+=+11
She has 11 $1 bills, 8 $5 bills, and 5 $20 bills
check answer:
(3) 1a+%2B+5b+%2B+20c+=+151
11+%2B+5%2A8+%2B+20%2A5+=+151
11+%2B+40+%2B+100+=+151
151+=+151
OK