There are 16 coins in a piggy bank. The coins are all nickels and dimes. All together the total amount of money in the bank is $1.05. How many of each coin are there?
N + D = 16
5N + 10D = 105
Multiply the first equation by 5 (both sides)
5N + 5D = 80
Now subtract the last equation from the one above.
5D = 25
D = 5
N = 11
To figure out how many nickels and dimes are in the piggy bank, we can create a system of equations based on the given information.
Let's say the number of nickels in the piggy bank is represented by 'N', and the number of dimes is represented by 'D'.
We know that there are 16 coins in total, so we can write the equation:
N + D = 16 ---(Equation 1)
We also know that the total value of the coins is $1.05. A nickel is worth $0.05, and a dime is worth $0.10. So, we can write the second equation:
0.05N + 0.10D = 1.05 ---(Equation 2)
Now, we need to solve this system of equations to find the values of 'N' and 'D'. There are different methods to do this, such as substitution or elimination. Let's use the substitution method:
Step 1: Rearrange Equation 1 to solve for N:
N = 16 - D ---(Equation 3)
Step 2: Substitute Equation 3 into Equation 2:
0.05(16 - D) + 0.10D = 1.05
Step 3: Solve for D:
0.80 - 0.05D + 0.10D = 1.05
0.05D = 1.05 - 0.80
0.05D = 0.25
D = 0.25 / 0.05
D = 5
Step 4: Substitute the value of D back into Equation 3 to find N:
N = 16 - 5
N = 11
Therefore, there are 11 nickels and 5 dimes in the piggy bank.