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.
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