SOLUTION: Diane has $1.20 in dimes and nickels. She has a total of 15 coins. How many of each kind does she have? Smallest Value Highest Value

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Question 747034: Diane has $1.20 in dimes and nickels. She has a total of 15 coins. How many of each kind does she have?
Smallest Value
Highest Value
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
-----------
(1) +n+%2B+d+=+15+
(2) +5n+%2B+10d+=+120+ ( in cents )
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Multiply both sides 0f (1) by +10+
and subtract (2) from (1)
(1) +10n+%2B+10d+=+150+
(2) +-5n+-+10d+=+-120+
+5n+=+30+
+n+=+6+
-----------
and, since
(1) +n+%2B+d+=+15+
(1) +6+%2B+d+=+15+
+d+=+9+
She has 6 nickels and 9 dimes
check:
(2) +5n+%2B+10d+=+120+
(2) +5%2A6+%2B+10%2A9+=+120+
(2) +30+%2B+90+=+120+
(2) +120+=+120+
OK