SOLUTION: Joe has a collection of nickles and dimes that is worth $7.05. If the number of dimes were doubled and the number of nickels were increased by 7, the value of the coins would be $1

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Question 585807: Joe has a collection of nickles and dimes that is worth $7.05. If the number of dimes were doubled and the number of nickels were increased by 7, the value of the coins would be $13.30. How many dimes does he have?
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
given:
(1) +5n+%2B+10d+=+705+ ( in cents )
(2) +5%2A%28+n+%2B+7+%29+%2B+10%2A%282d%29+=+1330+
--------
(2) +5n+%2B+35+%2B+20d+=+1330+
(2) +5n+%2B+20d+=+1295+
Subtract (1) from (2)
(2) +5n+%2B+20d+=+1295+
(1) +-5n+-+10d+=+-705+
+10d+=+590+
+d+=+59+
and, since
(1) +5n+%2B+10d+=+705+
(1) +5n+%2B+10%2A59+=+705+
(1) +5n+=+705+-+590+
(1) +5n+=+115+
(1) +n+=+23+
He has 23 nickels and 59 dimes
check:
(2) +5%2A%28+23+%2B+7+%29+%2B+10%2A%282%2A59%29+=+1330+
(2) +5%2A30+%2B+10%2A118+=+1330+
(2) +150+%2B+1180+=+1330+
(2) +1330+=+1330+
OK