SOLUTION: A coin bank contains only nickels and dimes. The total value of the coins in the bank is $2.45. If the nickels were dimes and the dimes were nickels, the total value of the coins w

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Question 521094: A coin bank contains only nickels and dimes. The total value of the coins in the bank is $2.45. If the nickels were dimes and the dimes were nickels, the total value of the coins would be $3.10. Find the number of nickels in the bank.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = number of nickels
Let b = number of dimes
If the nickels were dimes and the dimes
were nickels, then a changes to b
and b changes to a
given:
(1) +5a+%2B+10b+=+245+ ( in cents )
(2) +5b+%2B+10a+=+310+
Multiply both sides of (1) by 2
and subtract (2) from (1)
(1) +10a+%2B+20b+=+490+
(2) +-10a+-+5b+=+-310+
+15b+=+180+
+b+=+12+
and, since
(1) +5a+%2B+10b+=+245+
(1) +5a+%2B+10%2A12+=+245+
(1) +5a+%2B+120+=+245+
(1) +5a+=+125+
(1) +a+=+25+
There are 25 nickels in the bank
check:
(2) +5b+%2B+10a+=+310+
(2) +5%2A12+%2B+10%2A25+=+310+
(2) +60+%2B+250+=+310+
(2) +310+=+310+
OK