There are 7 coins in a piggy bank. The coins are all quarters and dimes. All together the total amount of money in the bank is $1.15. How many of each coin are in the piggy bank.
To solve this problem, we can set up a system of equations.
Let's use the variables 'q' to represent the number of quarters and 'd' to represent the number of dimes in the piggy bank.
Based on the information given, we can create two equations:
1) The total number of coins equation: q + d = 7
This equation represents the fact that there are 7 coins in the piggy bank.
2) The total value of the coins equation: 0.25q + 0.10d = 1.15
This equation represents the fact that the total value of the coins in the piggy bank is $1.15.
Now we can solve this system of equations to find the values of 'q' and 'd'.
We can use the first equation to solve for one variable in terms of the other. Let's solve for 'd' in terms of 'q':
q + d = 7
d = 7 - q
Now substitute this expression for 'd' in the second equation:
0.25q + 0.10(7 - q) = 1.15
Now solve the equation for 'q':
0.25q + 0.70 - 0.10q = 1.15
0.15q + 0.70 = 1.15
0.15q = 1.15 - 0.70
0.15q = 0.45
Divide both sides of the equation by 0.15:
q = 0.45 / 0.15
q = 3
So there are 3 quarters in the piggy bank.
Now substitute this value back into the first equation to solve for 'd':
3 + d = 7
d = 7 - 3
d = 4
So there are 4 dimes in the piggy bank.
Therefore, there are 3 quarters and 4 dimes in the piggy bank.