Final answer:
Gaby has 28 quarters and 39 nickels in her piggy bank. We determined this by setting up and solving a system of equations based on the values of the coins and the total number of coins she has.
Step-by-step explanation:
To solve for the number of quarters and nickels in Gaby's piggy bank, we can set up a system of equations based on the values and quantities of the coins. Let q represent the number of quarters and n represent the number of nickiles. Since each quarter is worth $0.25 and each nickel is worth $0.05, we can represent the total value as 0.25q + 0.05n = $8.95. Additionally, since we know the total number of coins is 67, we can represent this with the equation q + n = 67.
Step-by-step, we can solve the system:
- 0.25q + 0.05n = $8.95
- q + n = 67
Now we can multiply the second equation by 0.05 to align the nickel value: 0.05q + 0.05n = 3.35. Subtracting this new equation from the first gives us: 0.20q = $8.95 - $3.35. Solving for q, we find that q = ($8.95 - $3.35) / 0.20, which simplifies to q = 28. Thus, Gaby has 28 quarters.
Using q = 28 in the second original equation, n + 28 = 67, we find n = 67 - 28, which means Gaby has 39 nickels.