Final answer:
Gaby has 21 nickels and 20 quarters in her piggy bank. By setting up and solving a system of equations based on the value and number of coins, the quantities of each coin type are determined.
Step-by-step explanation:
Gaby's piggy bank contains nickels and quarters worth $6.05. If she has 41 coins in all, we can set up two equations to solve this problem using algebra.
Let's denote the number of nickels as N and the number of quarters as Q. The first equation based on the total value of coins is 0.05N + 0.25Q = 6.05. The second equation based on the total number of coins is N + Q = 41.
Now, we can solve the system of equations. First, rearrange the second equation to Q = 41 - N and substitute it into the first equation:
- 0.05N + 0.25(41 - N) = 6.05
- 0.05N + 10.25 - 0.25N = 6.05
- -0.20N = -4.20
- N = 21
Now that we know there are 21 nickels, we can find the number of quarters by substituting N in the second equation:
Therefore, Gaby has 21 nickels and 20 quarters in her piggy bank.