SOLUTION: Christina makes $9.25 purchase at a bookstore, with a $20.00 bill the gives her the change in dollars and quarters coins. There are 19 coins in all. How many of each kind are ther

Algebra ->  Linear-equations -> SOLUTION: Christina makes $9.25 purchase at a bookstore, with a $20.00 bill the gives her the change in dollars and quarters coins. There are 19 coins in all. How many of each kind are ther      Log On


   



Question 888195: Christina makes $9.25 purchase at a bookstore, with a $20.00 bill the gives her the change in dollars and quarters coins. There are 19 coins in all. How many of each kind are there?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of dollar coins
Let +b+ = number of quarters
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(1) +a+%2B+b+=+19+
(2) +100a+%2B+25b+=+2000+-+925+ ( in cents )
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(2) +100a+%2B+25b+=+1075+
Multiply both sides of (1) by +25+
and subtract (1) from (2)
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(2) +100a+%2B+25b+=+1075+
(1) +-25a+-+25b+=+-475+
+75a+=+600+
+a+=+8+
and, since,
(1) +a+%2B+b+=+19+
(1) +b+=+11+
There are 8 dollar coins
There are 11 quarters
check:
(2) +100%2A8+%2B+25%2A11+=+2000+-+925+
(2) +800+%2B+275+=+1075+
(2) +1075+=+1075+
OK