SOLUTION: Tim has twice as much money in nickels as in dimes. He has 30 coins in all. How many of each coin does he have?

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Question 1092835: Tim has twice as much money in nickels as in dimes. He has 30 coins in all. How many of each coin does he have?
Found 3 solutions by JoelSchwartz, ikleyn, greenestamps:
Answer by JoelSchwartz(130)   (Show Source): You can put this solution on YOUR website!
x=the number of nickels
y=the number of dimes
.05x=2(.1y)
.05x=.2y
x+y=30
x=30-y
.05(30-y)=.2y
1.5-.05y=.2y
1.5=.25y
6=y
x=30-6
x=24
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.
Let N be the number of nickels.
Then the number of dimes is (30-N).

Amount of money (cents) in nickels is  5*N.
Amount of money (cents) in dimes   is 10*(30-N).

The condition says

5N = 2*(10*(30-N)).


It is your equation to solve. Simplify and find N:

5N = 20*(30-N)  ====>  5N = 600 - 20N  ====>  5N + 20N = 600  ====>  25N = 600  ====>  N =  = 24.


Answer.  24 nickels and 6  = 30-24 dimes.


Check   Amount in nickels = 5*24 = 120 cents.
        Amount in dimes = 10*6 = 60 cents.    ! Correct !.


Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Since the amount of money he has in nickels is twice the amount he has in dimes, and since each nickel is worth only half as much as each dime, we can deduce that the number of nickels he has is 4 times the number of dimes.

Then, since there are 30 coins in all, if we call the number of dimes d then




So he has 6 dimes and 24 nickels.
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