Final answer:
There are 4 nickels, 12 dimes, and 9 quarters in the piggy bank.
Step-by-step explanation:
To solve this problem, let's assign variables to represent the number of nickels, dimes, and quarters. Let's say the number of nickels is 'n', dimes is 'd', and quarters is 'q'.
According to the information given, the total value of the coins is $3.65. We can express this information as an equation: 5n + 10d + 25q = 365 (since there are 100 pennies in a dollar).
We are also given that the number of dimes is three times greater than the number of nickels, so we can write the equation d = 3n.
And the number of quarters is one greater than double the number of nickels, so q = 2n + 1.
Now we have a system of equations. Substituting the values of d and q in terms of n into the first equation, we get 5n + 10(3n) + 25(2n + 1) = 365.
Simplifying this equation, we get 5n + 30n + 50n + 25 = 365.
Combining like terms, we get 85n + 25 = 365. Subtracting 25 from both sides, we have 85n = 340. Dividing both sides by 85, we find n = 4.
Therefore, there are 4 nickels, 3(4) = 12 dimes, and 2(4) + 1 = 9 quarters in the piggy bank.