SOLUTION: Mrs. Sanders had 80 coins. Some of them were $1.00 coins and the rest were .50 cent coins. The total amount added up to $50.00. How many coins of each kind were there?

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Question 808802: Mrs. Sanders had 80 coins. Some of them were $1.00 coins and the rest were .50 cent coins. The total amount added up to $50.00. How many coins of each kind were there?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of $1 coins
Let +b+ = number of $.50 coins
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(1) +a+%2B+b+=+80+
(2) +1%2Aa+%2B+.5%2Ab+=+50+
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(1) +b+=+80+-+a+
Substitute this into (2)
(2) a+%2B+.5%2A%28+80+-+a+%29+=+50+
(2) +a+%2B+40+-+.5a+=+50+
(2) +.5a+=+50+-+40+
(2) +.5a+=+10+
(2) +a+=+20+
and, since
(1) +a+%2B+b+=+80+
(1) +b+=+60+
There are 20 $1 coins and 60 $.50 coins
check:
(2) +1%2A20+%2B+.5%2A60+=+50+
(2) +20+%2B+30+=+50+
(2) +50+=+50+
OK