Final answer:
To solve the problem, set up an equation using the given information. Solve the equation to find the values of x and 2x + 3, representing the number of dimes and nickels.
Step-by-step explanation:
Let's assume the number of dimes in the bank is x. According to the problem, there are 3 more than twice as many nickels as there are dimes, which means the number of nickels is 2x + 3.
The total value of the dimes can be calculated by multiplying the number of dimes (x) by 0.10, and the total value of the nickels can be calculated by multiplying the number of nickels (2x + 3) by 0.05. Setting up the equation, we have 0.10x + 0.05(2x + 3) = 9.15. Solving this equation will give us the values of x and 2x + 3, which represent the number of dimes and nickels in the bank respectively.