Question

adrianna has 16 dollars worth of quarters and dimes. If adriana has 2 and a half times as many dimes as she does quarters, how many quarters does she have?

Answer 1

Let the number of quarters Adrianna has be \( q \). Since she has 2.5 times as many dimes as quarters, the number of dimes can be represented as \( 2.5q \).

The value of the quarters can be calculated as:

\[
\text{Value of quarters} = 0.25q \quad \text{(since each quarter is worth $0.25)}
\]

The value of the dimes can be calculated as:

\[
\text{Value of dimes} = 0.10(2.5q) = 0.25q \quad \text{(since each dime is worth $0.10)}
\]

Now, we can find the total value:

\[
\text{Total value} = \text{Value of quarters} + \text{Value of dimes} = 0.25q + 0.25q = 0.50q
\]

According to the problem, this total value equals $16:

\[
0.50q = 16
\]

To find \( q \), we can divide both sides by 0.50:

\[
q = \frac{16}{0.50} = 32
\]

So, Adrianna has \( \boxed{32} \) quarters.

To verify this, we can calculate the number of dimes:

\[
\text{Number of dimes} = 2.5 \times 32 = 80
\]

Calculating the total value:

\[
\text{Value of quarters} = 32 \times 0.25 = 8 \quad \text{(total value from quarters)}
\]
\[
\text{Value of dimes} = 80 \times 0.10 = 8 \quad \text{(total value from dimes)}
\]

Now, adding these values together:

\[
8 + 8 = 16
\]

Thus, the calculations confirm that the answer \( \boxed{32} \) quarters is correct.