Alycia's pggy bank has dimes and quarters in it. The numbers of dimes is four less than three times the number of quarters. If the total value of the coins is $7.85, how many dimes are in the piggy bank?
q = number of quarters
3q - 4 = number of dimes
0.25q = value of quarters
0.10(3q - 4) = value of dimes
0.25q + 0.10(3q - 4) = 7.85
Solve for q, number of quarters
3q - 4 = number of dimes
To find the number of dimes in Alycia's piggy bank, you can use algebraic equations. Let's assign variables to the number of dimes and quarters. Let `d` represent the number of dimes and `q` represent the number of quarters.
According to the problem, the number of dimes is four less than three times the number of quarters:
d = 3q - 4
Next, we need to consider the total value of the coins. The value of a dime is $0.10, and the value of a quarter is $0.25.
The total value of the coins is given as $7.85. We can express this in terms of dimes and quarters:
0.10d + 0.25q = 7.85
Now we have a system of two equations:
d = 3q - 4
0.10d + 0.25q = 7.85
We can solve this system of equations to find the values of d and q.
First, let's substitute the value of d from the first equation into the second equation:
0.10(3q - 4) + 0.25q = 7.85
Simplifying this equation:
0.30q - 0.40 + 0.25q = 7.85
0.55q - 0.40 = 7.85
0.55q = 8.25
q = 8.25 / 0.55
q = 15
Now that we have the value of q, we can substitute it back into the first equation to find the value of d:
d = 3(15) - 4
d = 45 - 4
d = 41
Therefore, there are 41 dimes in Alycia's piggy bank.