Let the number of quarters Sam has be \( q \). Since Sam has 9 more nickels than quarters, the number of nickels he has will be \( q + 9 \).
The value of the quarters in cents is \( 25q \) (since each quarter is worth 25 cents), and the value of the nickels in cents is \( 5(q + 9) \) (since each nickel is worth 5 cents).
According to the problem, the total amount of money Sam has is $2.55, which is equal to 255 cents. Thus, we can set up the following equation:
\[ 25q + 5(q + 9) = 255 \]
Now, we will simplify the equation:
- Distribute the 5: \[ 25q + 5q + 45 = 255 \]
- Combine like terms: \[ 30q + 45 = 255 \]
- Subtract 45 from both sides: \[ 30q = 255 - 45 \] \[ 30q = 210 \]
- Divide both sides by 30: \[ q = \frac{210}{30} = 7 \]
Now that we have the number of quarters, we can find the number of nickels:
\[ n = q + 9 = 7 + 9 = 16 \]
Thus, Sam has \( 7 \) quarters and \( 16 \) nickels.
To confirm our solution, we can check the value of the coins:
- The value of the quarters is \( 7 \times 25 = 175 \) cents.
- The value of the nickels is \( 16 \times 5 = 80 \) cents.
Adding these values together: \[ 175 + 80 = 255 \text{ cents}, \] which confirms that our solution is correct.
Therefore, the final answer is:
- Number of quarters: \( 7 \)
- Number of nickels: \( 16 \)