SOLUTION: Ava has 52 coins. The value of her coins (only dimes and nickels) is $4.15. Find the number of nickels and the number of dimes.

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Question 808297: Ava has 52 coins. The value of her coins (only dimes and nickels) is $4.15. Find the number of nickels and the number of dimes.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = number of nickels
Let +d+ = number of dimes
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(1) +5n+%2B+10d+=+415+ ( in cents )
(2) +n+%2B+d+=+52+
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Multiply both sides of (2) by +5+ and
subtract (2) from (1)
(1) +5n+%2B+10d+=+415+
(2) +-5n+-+5d+=+-260+
+5d+=+155+
+d+=+31+
and, since
(2) +n+%2B+d+=+52+
(2) +n+=+21+
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There are 21 nickels and 31 dimes
check:
(1) +5%2A21+%2B+10%2A31+=+415+
(1) +105+%2B+310+=+415+
(1) +415+=+415+
OK