SOLUTION: Andrew has $446 in ten dollar, five dollar, and one dollar bills. There were 94 bills in all, and 10 more five dollar bills than ten dollar bills. How many one dollar bills did And

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Question 408137: Andrew has $446 in ten dollar, five dollar, and one dollar bills. There were 94 bills in all, and 10 more five dollar bills than ten dollar bills. How many one dollar bills did Andrew have?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
t = number of $10 bills
f = number of $5 bills
n = number of $1 bills
given:
(1) 10t+%2B+5f+%2B+1n+=+446
(2) t+%2B+f+%2B+n+=+94
(3) f+=+t+%2B+10
There are 3 equations and 3 unknowns,
so it's solvable
Subtract (2) from (1)
(1) 10t+%2B+5f+%2B+1n+=+446
(2) -t+-+f+-+n+=+-94
9t+%2B+4f+=+352
Substitute (3) into the result
9t+%2B+4%2A%28t+%2B+10%29+=+352
9t+%2B+4t+%2B+40+=+352
13t+=+312
t+=+24
and, since
f+=+t+%2B+10
f+=+34
and
(2) t+%2B+f+%2B+n+=+94
24+%2B+34+%2B+n+=+94
n=+94+-+58
n+=+36
Andrew had 36 $1 bills
check answer:
(1) 10t+%2B+5f+%2B+1n+=+446
(1) 10%2A24+%2B+5%2A34+%2B+1%2A36+=+446
240+%2B+170+%2B+36+=+446
446+=+446
OK