Final answer:
To find the number of nickels and quarters in the vending machine, we can set up a system of equations. By solving these equations, we find that there are 8 nickels and 19 quarters in the machine.
Step-by-step explanation:
Let's assign variables to the number of quarters and nickels in the vending machine. Let Q represent the number of quarters and N represent the number of nickels.
According to the problem, there are three more than two times as many quarters as nickels, so we can write the equation: Q = 2N + 3.
Also, the total value of the coins is $5.15, which can be expressed as the equation: 0.25Q + 0.05N = 5.15.
Now we can solve these two equations simultaneously to find the values of Q and N. Substituting the first equation into the second equation, we get: 0.25(2N + 3) + 0.05N = 5.15.
Simplifying this equation, we have: 0.50N + 0.75 + 0.05N = 5.15.
Combining like terms, we get: 0.55N + 0.75 = 5.15.
Subtracting 0.75 from both sides, we have: 0.55N = 4.40.
Dividing both sides by 0.55, we find: N = 8.
Substituting this value back into the first equation, we get: Q = 2(8) + 3 = 19.
Therefore, there are 8 nickels and 19 quarters in the vending machine.