SOLUTION: Raleigh has a total of 66 coins, all of which are either dimes or nickles. The total value of the coins is $5.75. Find the number of each type of coin.

Algebra ->  Algebra  -> Human-and-algebraic-language -> SOLUTION: Raleigh has a total of 66 coins, all of which are either dimes or nickles. The total value of the coins is $5.75. Find the number of each type of coin.      Log On

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Question 183629: Raleigh has a total of 66 coins, all of which are either dimes or nickles. The total value of the coins is $5.75. Find the number of each type of coin.
Answer by eperette(173) About Me  (Show Source):
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Let n = number of nickels
d = number of dimes
n + d = 66
0.05n + 0.10d = 5.75
We will solve by using substitution
n + d = 66
n + d - d = 66 - d
n = 66 - d
then
0.05n + 0.10d = 5.75
0.05(66 - d) + 0.10d = 5.75
3.3 - 0.05d + 0.10d = 5.75
3.3 + 0.05d = 5.75
3.3- 3.3 + 0.05d = 5.75 - 3.3
0.05d = 2.45
0.05d/0.05= 2.45/0.05
d = 49
and n = 66 -d = 66 - 49 = 17
answer: there are 49 dimes and 17 nickels