Question

Sam has $2.55 in quarters and nickels. He has 9 more nickels than quarters. How many nickels and quarters does he have?

Answer 1

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:

1. Distribute the 5:
\[
25q + 5q + 45 = 255
\]
2. Combine like terms:
\[
30q + 45 = 255
\]
3. Subtract 45 from both sides:
\[
30q = 255 - 45
\]
\[
30q = 210
\]
4. 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: \( 16 \)