SOLUTION: Jorge has a total of 50 coins, all of which are either dimes or nickels. The total value of the coins is $4.15. Find the number of each type of coin.

Question 985912: Jorge has a total of 50 coins, all of which are either dimes or nickels. The total value of the coins is $4.15. Find the number of each type of coin.
Found 2 solutions by macston, ikleyn:
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
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D=number of dimes; N=number of nickels
.
D+N=50
D=50-N
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$0.05N+$0.10D=$4.15
$0.05N+$0.10(50-N)=$4.15
$0.05N+$5.00-$0.10N=$4.15
-$0.05N=-$0.85
N=17 ANSWER 1: There were 17 nickels.
D=50-N=50-17=33 ANSWER 2: There were 33 dimes.
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CHECK:
$0.05N+$0.10D=$4.15
$0.05(17)+$0.10(33)=$4.15
$0.85+$3.30=$4.15
$4.15=$4.15
Answer by ikleyn(52810)   (Show Source): You can put this solution on YOUR website!
.
Let n be the number of nickels Jorge has.
Then the number of dimes is 50-n.

So, Jorge has 5*n cents in nickels and 10*(50-n) cents in dimes.

In total, it is $4.15, which gives you an equation

5*n + 10*(50-n) = 415.

Solve it step by step:

5n + 500 - 10n = 415,

5n - 10n = 415 - 500,

-5n = -85,

n = = = 17.

Thus Jorge has 17 nickels and 50-17 = 33 dimes.

Check: 17*5 + 33*10 = 85 + 330 = 415.     Correct!

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