SOLUTION: Katie has 30 coins. Some are dimes and some are nickels. In all she has $2.10. How many nickels and dimes does she have?

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Question 536473: Katie has 30 coins. Some are dimes and some are nickels. In all she has $2.10. How many nickels and dimes does she have?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let d = number of dimes
Let n = number of nickels
given:
(1) +d+%2B+n+=+30+
(2) +10d+%2B+5n+=+210+ ( in cents )
-----------------
Multiply both sides of (1) by 5
then subtract (1) from (2)
(2) +10d+%2B+5n+=+210+
(1) +-5d+-+5n+=+-150+
+5d+=+60+
+d+=+12+
and, since
(1) +d+%2B+n+=+30+
(1) +12+%2B+n+=+30+
(1) +n+=+30+-+12+
(1) +n+=+18+
She has 12 dimes and 18 nickels
check:
(2) +10%2A12+%2B+5%2A18+=+210+
(2) +120+%2B+90+=+210+
(2) +210+=+210+
OK