SOLUTION: Raleigh has a total of 54 coins, all of which are either dimes or nickels. The total value is $4.30. Find the number of each type of coin.

Question 241624: Raleigh has a total of 54 coins, all of which are either dimes or nickels. The total value is $4.30. Find the number of each type of coin.
Answer by kelli_scofield(5) (Show Source): You can put this solution on YOUR website!
I am going to set this problem up with two equations.
Equation 1:
n+d=54
Equation 2:
.05n+.10d=4.30
The first equation signifies the number of coins. n=nickels and d=dimes.
The second equation signifies the worth of the coins.
First, I am going to make equation #2 simpler by moving the decimal place on each term two units to the right. My new equation number 2 is 5n+10d=430
Now, the two equations are:
(Equation 1)n+d=54
(Equation 2)5n+10d=430
Using elimination, I am going to multiply equation #1 by -5(negative 5).
This gives me:
(Equation 1)-5n-5d=-270
(Equation 2) 5n+10d=430
Adding the two equations, the n's get cancelled.
Now you have one equation of:
5d=160
Dividing the equation by 5 gives you: d=32
Plug (32) for d in one of the original equations.
n+d=54
n+(32)=54
After subtracting 32, you get n=22.
So, your answer is 22 nickels and 32 dimes.
You can check your answer by plugging both of these values in for each of the original equations.
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